Hyers-Ulam-Rassias stability of high-dimensional quaternion impulsive fuzzy dynamic equations on time scales

Chao Wang; Zhien Li; Ravi P. Agarwal

doi:10.3934/dcdss.2021041

Previous Article
Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations
DCDS-S Home
This Issue
Next Article
Controllability of Sobolev type fuzzy differential equation with non-instantaneous impulsive condition

doi: 10.3934/dcdss.2021041

Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Hyers-Ulam-Rassias stability of high-dimensional quaternion impulsive fuzzy dynamic equations on time scales

Chao Wang ^1, , Zhien Li ^1, and Ravi P. Agarwal ^2,3,,

1.	Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
2.	Department of Mathematics, Texas A & M University-Kingsville, 700 University Blvd., TX 78363-8202, Kingsville, TX, USA
3.	Distinguished University Professor of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA

^* Corresponding author: Ravi P. Agarwal

Received January 2021 Early access April 2021

Fund Project: This work is supported by Youth Fund of NSFC (No. 11961077)

In this paper, the Hyers-Ulam-Rassias stability of high-dimensional quaternion fuzzy dynamic equations with impulses is first considered on time scales. Some fundamental calculus results of the high-dimensional fuzzy quaternion functions in fuzzy quaternion space are established. Based on it, some sufficient conditions are obtained to guarantee the Hyers-Ulam-Rassias stability of the quaternion impulsive fuzzy dynamic equations in high-dimensional case. Moreover, several examples are provided to show the feasibility of our main results on various types of time scales.

Keywords: Impulsive fuzzy dynamic equations, Hyers-Ulam-Rassias stability, Quaternion space, Time Scales.

Mathematics Subject Classification: Primary: 34A07, 34N05; Secondary: 11R52.

Citation: Chao Wang, Zhien Li, Ravi P. Agarwal. Hyers-Ulam-Rassias stability of high-dimensional quaternion impulsive fuzzy dynamic equations on time scales. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2021041

References:

[1]	R. P. Agarwal, S. Arshad, D. O'Regan and V. Lupulescu, Fuzzy fractional integral equations under compactness type condition, Fract. Calc. Appl. Anal., 15 (2012), 572-590. doi: 10.2478/s13540-012-0040-1. Google Scholar
[2]	B. Bede and S. G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Sets Syst., 147 (2004), 385-403. doi: 10.1016/j.fss.2003.08.004. Google Scholar
[3]	B. Bede and L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets Syst., 230 (2013), 119-141. doi: 10.1016/j.fss.2012.10.003. Google Scholar
[4]	M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications. Birkhauser, Boston, 2001. doi: 10.1007/978-1-4612-0201-1. Google Scholar
[5]	J. J. Buckley, Fuzzy complex numbers, Fuzzy Sets and Syst., 33 (1989), 333-345. doi: 10.1016/0165-0114(89)90122-X. Google Scholar
[6]	S. Bernstein, Topics in Clifford Analysis, Special Volume in Honor of Wolfgang Sprößig, Trends in Mathematics, Birkhäuser, 2019. Google Scholar
[7]	D. Cheng, K. I. Kou and Y. H. Xia, A unified analysis of linear quaternion dynamic equations on time scales, J. Appl. Anal. Compt., 8 (2018), 172-201. doi: 10.11948/2018.172. Google Scholar
[8]	Z. Cai and K. I. Kou, Laplace transform: A new approach in solving linear quaternion differential equations, Math. Meth. Appl. Sci., 41 (2018), 4033-4048. doi: 10.1002/mma.4415. Google Scholar
[9]	P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets, World Scientific, Singapore, 1994. doi: 10.1142/2326. Google Scholar
[10]	T. Fang and J. Sun, Stability of complex-valued impulsive system with delay, Applied Mathematics and Computation, 240 (2014), 102-108. doi: 10.1016/j.amc.2014.04.062. Google Scholar
[11]	T. Fang and J. Sun, Stability of complex-valued impulsive and switching system and application to the Lü system, Nonlinear Anal.: Hybrid Syst., 14 (2014), 38-46. doi: 10.1016/j.nahs.2014.04.004. Google Scholar
[12]	S. Georgiev and J. Morais, An introduction to the Hilger quaternion numbers, AIP Conference Proceedings, 1558 (2013), 550-553. doi: 10.1063/1.4825549. Google Scholar
[13]	D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27 (1941), 222-224. doi: 10.1073/pnas.27.4.222. Google Scholar
[14]	D. H. Hyers, G. Isac and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, 1998. doi: 10.1007/978-1-4612-1790-9. Google Scholar
[15]	S. Hilger, Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten (PhD Thesis), Universität Würzburg, 1989. Google Scholar
[16]	S. M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001. Google Scholar
[17]	A. Khastan and R. Rodríguez-López, On periodic solutions to first order linear fuzzy differential equations under differential inclusions' approach, Inf. Sci., 322 (2015), 31-50. doi: 10.1016/j.ins.2015.06.003. Google Scholar
[18]	A. Khastan, New solutions for first order linear fuzzy difference equations, J. Comput. Appl. Math., 312 (2017), 156-166. doi: 10.1016/j.cam.2016.03.004. Google Scholar
[19]	O. Kaleva, A note on fuzzy differential equations, Nonlinear Anal., 64 (2006), 895-900. doi: 10.1016/j.na.2005.01.003. Google Scholar
[20]	K. I. Kou and Y. Xia, Linear quaternion differential equations: Basic theory and fundamental results, Studies. Appl. Math., 141 (2018), 3-45. doi: 10.1111/sapm.12211. Google Scholar
[21]	Z. Li, C. Wang, R. P. Agarwal and D. O'Regan, Commutativity of quaternion-matrix-valued functions and quaternion matrix dynamic equations on time scales, Stud. Appl. Math., 146 (2021), 139-210. doi: 10.1111/sapm.12344. Google Scholar
[22]	Z. Li and C. Wang, Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales, Open Math., 18 (2020), 353-377. doi: 10.1515/math-2020-0021. Google Scholar
[23]	R. Liu, J. Wang and D. O'Regan, Ulam type stability of first-order linear impulsive fuzzy differential equations, Fuzzy Sets and Syst., 400 (2020), 34-89. doi: 10.1016/j.fss.2019.10.007. Google Scholar
[24]	V. Lupulescu, Fractional calculus for interval-valued functions, Fuzzy Sets Syst., 265 (2015), 63-85. doi: 10.1016/j.fss.2014.04.005. Google Scholar
[25]	V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. doi: 10.1142/0906. Google Scholar
[26]	R. P. A. Moura, F. B. Bergamaschi, R. H. N. Santiago and B. R. C. Bedregal, Fuzzy quaternion numbers, FUZZ-IEEE, (2013), 1–6. doi: 10.1109/FUZZ-IEEE.2013.6622400. Google Scholar
[27]	T. Miura, S. Miyajima and S. E. Takahasi, A characterization of Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl., 286 (2003), 136-146. doi: 10.1016/S0022-247X(03)00458-X. Google Scholar
[28]	R. E. Moore, Interval Analysis, Prentice Hall, New Jersey, 1966. Google Scholar
[29]	J. J. Nieto and R. Rodríguez-López, Bounded solutions for fuzzy differential and integral equations, Chaos Solitons & Frac., 27 (2006), 1376-1386. doi: 10.1016/j.chaos.2005.05.012. Google Scholar
[30]	D. Ramot, R. Milo, M. Friedman and A. Kandel, Complex fuzzy sets, IEEE Transactions on Fuzzy Syst., 10 (2002), 171-186. Google Scholar
[31]	T. M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Am. Math. Soc., 72 (1978), 297-300. doi: 10.1090/S0002-9939-1978-0507327-1. Google Scholar
[32]	I. A. Rus, Ulam stabilities of ordinary differential equations in a Banach space, Carpath. J. Math., 26 (2010), 103-107. Google Scholar
[33]	R. Rodríguez-López, Monotone method for fuzzy differential equations, Fuzzy Sets and Syst., 159 (2008), 2047-2076. doi: 10.1016/j.fss.2007.12.020. Google Scholar
[34]	R. Rodríguez-López, Periodic boundary value problems for impulsive fuzzy differential equations, Fuzzy Sets and Syst., 159 (2008), 1384-1409. doi: 10.1016/j.fss.2007.09.005. Google Scholar
[35]	L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets Syst., 161 (2010), 1564-1584. doi: 10.1016/j.fss.2009.06.009. Google Scholar
[36]	Y. Shen, On the Ulam stability of first order linear fuzzy differential equations under generalized differentiability, Fuzzy Sets Syst., 280 (2015), 27-57. doi: 10.1016/j.fss.2015.01.002. Google Scholar
[37]	D. E. Tamir, L. Jin and A. Kandel, A new interpretation of complex membership grade, J. Intelligent and Fuzzy Syst., 26 (2011), 285-312. doi: 10.1002/int.20454. Google Scholar
[38]	S. M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8 Interscience Publishers, New York-London, 1960. Google Scholar
[39]	C. Wang, R. P. Agarwal and D. O'Regan, Calculus of fuzzy vector-valued functions and almost periodic fuzzy vector-valued functions on time scales, Fuzzy Sets and Syst., 375 (2019), 1-52. doi: 10.1016/j.fss.2018.12.008. Google Scholar
[40]	C. Wang, R. P. Agarwal and D. O'Regan, $\Pi$-semigroup for invariant under translations time scales and abstract weighted pseudo almost periodic functions with applications, Dyna. Syst. Appl., 25 (2016), 1-28. Google Scholar
[41]	C. Wang, R. P. Agarwal and R. Sakthivel, Almost periodic oscillations for delay impulsive stochastic Nicholson's blowflies timescale model, Comput. Appl. Math., 37 (2018), 3005-3026. doi: 10.1007/s40314-017-0495-0. Google Scholar
[42]	C. Wang, G. Qin, R. P. Agarwal and D. O'Regan, $\Diamond_{\alpha}$-Measurability and combined measure theory on time scales, Applic. Anal., 2020. doi: 10.1080/00036811.2020.1820997. Google Scholar
[43]	C. Wang, R. P. Agarwal and D. O'Regan, $n_0$-order $\Delta$-almost periodic functions and dynamic equations, Applic. Anal., 97 (2018), 2626-2654. doi: 10.1080/00036811.2017.1382689. Google Scholar
[44]	C. Wang, R. P. Agarwal, D. O'Regan and R. Sakthivel, Theory of Translation Closedness for Time Scales, , Springer, Developments in Mathematics Series, Volume 62, Switzerland, 2020. doi: 10.1007/978-3-030-38644-3. Google Scholar
[45]	C. Wang and R. P. Agarwal, Almost periodic solution for a new type of neutral impulsive stochastic Lasota-Wazewska timescale model, Appl. Math. Lett., 70 (2017), 58-65. doi: 10.1016/j.aml.2017.03.009. Google Scholar
[46]	C. Wang and R. P. Agarwal, Almost automorphic functions on semigroups induced by complete-closed time scales and application to dynamic equations, Discrt. Contin. Dynam. Syst. B, 25 (2020), 781-798. doi: 10.3934/dcdsb.2019267. Google Scholar
[47]	J. Wang, M. Fěckan and Y. Zhou, Ulam's type stability of impulsive ordinary differential equations, J. Math. Anal. Appl., 395 (2012), 258-264. doi: 10.1016/j.jmaa.2012.05.040. Google Scholar
[48]	X. X. Hu and K. I. Kou, Quaternion Fourier and linear canonical inversion theorems, Math. Meth. Appl. Sci., 40 (2017), 2421-2440. doi: 10.1002/mma.4148. Google Scholar
[49]	Y. Xia, C. Jahanchahi and D. P. Mandic, Quaternion-valued echo state networks, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 663-673. doi: 10.1109/TNNLS.2014.2320715. Google Scholar
[50]	Z. P. Yang, T. Z. Xu and M. Qi, Ulam-Hyers stability for fractional differential equations in quaternionic analysis, Adv. Appl. Clifford Algebras, 26 (2016), 469-478. doi: 10.1007/s00006-015-0576-3. Google Scholar
[51]	Z. P. Yang, T. Z. Xu and M. Qi, The Cauchy problem for quaternion fuzzy fractional differential equations, J. Intelligent & Fuzzy Syst., 29 (2015), 451-461. doi: 10.3233/IFS-151612. Google Scholar

show all references

References:

[1]	R. P. Agarwal, S. Arshad, D. O'Regan and V. Lupulescu, Fuzzy fractional integral equations under compactness type condition, Fract. Calc. Appl. Anal., 15 (2012), 572-590. doi: 10.2478/s13540-012-0040-1. Google Scholar
[2]	B. Bede and S. G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Sets Syst., 147 (2004), 385-403. doi: 10.1016/j.fss.2003.08.004. Google Scholar
[3]	B. Bede and L. Stefanini, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets Syst., 230 (2013), 119-141. doi: 10.1016/j.fss.2012.10.003. Google Scholar
[4]	M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications. Birkhauser, Boston, 2001. doi: 10.1007/978-1-4612-0201-1. Google Scholar
[5]	J. J. Buckley, Fuzzy complex numbers, Fuzzy Sets and Syst., 33 (1989), 333-345. doi: 10.1016/0165-0114(89)90122-X. Google Scholar
[6]	S. Bernstein, Topics in Clifford Analysis, Special Volume in Honor of Wolfgang Sprößig, Trends in Mathematics, Birkhäuser, 2019. Google Scholar
[7]	D. Cheng, K. I. Kou and Y. H. Xia, A unified analysis of linear quaternion dynamic equations on time scales, J. Appl. Anal. Compt., 8 (2018), 172-201. doi: 10.11948/2018.172. Google Scholar
[8]	Z. Cai and K. I. Kou, Laplace transform: A new approach in solving linear quaternion differential equations, Math. Meth. Appl. Sci., 41 (2018), 4033-4048. doi: 10.1002/mma.4415. Google Scholar
[9]	P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets, World Scientific, Singapore, 1994. doi: 10.1142/2326. Google Scholar
[10]	T. Fang and J. Sun, Stability of complex-valued impulsive system with delay, Applied Mathematics and Computation, 240 (2014), 102-108. doi: 10.1016/j.amc.2014.04.062. Google Scholar
[11]	T. Fang and J. Sun, Stability of complex-valued impulsive and switching system and application to the Lü system, Nonlinear Anal.: Hybrid Syst., 14 (2014), 38-46. doi: 10.1016/j.nahs.2014.04.004. Google Scholar
[12]	S. Georgiev and J. Morais, An introduction to the Hilger quaternion numbers, AIP Conference Proceedings, 1558 (2013), 550-553. doi: 10.1063/1.4825549. Google Scholar
[13]	D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27 (1941), 222-224. doi: 10.1073/pnas.27.4.222. Google Scholar
[14]	D. H. Hyers, G. Isac and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, 1998. doi: 10.1007/978-1-4612-1790-9. Google Scholar
[15]	S. Hilger, Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten (PhD Thesis), Universität Würzburg, 1989. Google Scholar
[16]	S. M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001. Google Scholar
[17]	A. Khastan and R. Rodríguez-López, On periodic solutions to first order linear fuzzy differential equations under differential inclusions' approach, Inf. Sci., 322 (2015), 31-50. doi: 10.1016/j.ins.2015.06.003. Google Scholar
[18]	A. Khastan, New solutions for first order linear fuzzy difference equations, J. Comput. Appl. Math., 312 (2017), 156-166. doi: 10.1016/j.cam.2016.03.004. Google Scholar
[19]	O. Kaleva, A note on fuzzy differential equations, Nonlinear Anal., 64 (2006), 895-900. doi: 10.1016/j.na.2005.01.003. Google Scholar
[20]	K. I. Kou and Y. Xia, Linear quaternion differential equations: Basic theory and fundamental results, Studies. Appl. Math., 141 (2018), 3-45. doi: 10.1111/sapm.12211. Google Scholar
[21]	Z. Li, C. Wang, R. P. Agarwal and D. O'Regan, Commutativity of quaternion-matrix-valued functions and quaternion matrix dynamic equations on time scales, Stud. Appl. Math., 146 (2021), 139-210. doi: 10.1111/sapm.12344. Google Scholar
[22]	Z. Li and C. Wang, Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales, Open Math., 18 (2020), 353-377. doi: 10.1515/math-2020-0021. Google Scholar
[23]	R. Liu, J. Wang and D. O'Regan, Ulam type stability of first-order linear impulsive fuzzy differential equations, Fuzzy Sets and Syst., 400 (2020), 34-89. doi: 10.1016/j.fss.2019.10.007. Google Scholar
[24]	V. Lupulescu, Fractional calculus for interval-valued functions, Fuzzy Sets Syst., 265 (2015), 63-85. doi: 10.1016/j.fss.2014.04.005. Google Scholar
[25]	V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. doi: 10.1142/0906. Google Scholar
[26]	R. P. A. Moura, F. B. Bergamaschi, R. H. N. Santiago and B. R. C. Bedregal, Fuzzy quaternion numbers, FUZZ-IEEE, (2013), 1–6. doi: 10.1109/FUZZ-IEEE.2013.6622400. Google Scholar
[27]	T. Miura, S. Miyajima and S. E. Takahasi, A characterization of Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl., 286 (2003), 136-146. doi: 10.1016/S0022-247X(03)00458-X. Google Scholar
[28]	R. E. Moore, Interval Analysis, Prentice Hall, New Jersey, 1966. Google Scholar
[29]	J. J. Nieto and R. Rodríguez-López, Bounded solutions for fuzzy differential and integral equations, Chaos Solitons & Frac., 27 (2006), 1376-1386. doi: 10.1016/j.chaos.2005.05.012. Google Scholar
[30]	D. Ramot, R. Milo, M. Friedman and A. Kandel, Complex fuzzy sets, IEEE Transactions on Fuzzy Syst., 10 (2002), 171-186. Google Scholar
[31]	T. M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Am. Math. Soc., 72 (1978), 297-300. doi: 10.1090/S0002-9939-1978-0507327-1. Google Scholar
[32]	I. A. Rus, Ulam stabilities of ordinary differential equations in a Banach space, Carpath. J. Math., 26 (2010), 103-107. Google Scholar
[33]	R. Rodríguez-López, Monotone method for fuzzy differential equations, Fuzzy Sets and Syst., 159 (2008), 2047-2076. doi: 10.1016/j.fss.2007.12.020. Google Scholar
[34]	R. Rodríguez-López, Periodic boundary value problems for impulsive fuzzy differential equations, Fuzzy Sets and Syst., 159 (2008), 1384-1409. doi: 10.1016/j.fss.2007.09.005. Google Scholar
[35]	L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets Syst., 161 (2010), 1564-1584. doi: 10.1016/j.fss.2009.06.009. Google Scholar
[36]	Y. Shen, On the Ulam stability of first order linear fuzzy differential equations under generalized differentiability, Fuzzy Sets Syst., 280 (2015), 27-57. doi: 10.1016/j.fss.2015.01.002. Google Scholar
[37]	D. E. Tamir, L. Jin and A. Kandel, A new interpretation of complex membership grade, J. Intelligent and Fuzzy Syst., 26 (2011), 285-312. doi: 10.1002/int.20454. Google Scholar
[38]	S. M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8 Interscience Publishers, New York-London, 1960. Google Scholar
[39]	C. Wang, R. P. Agarwal and D. O'Regan, Calculus of fuzzy vector-valued functions and almost periodic fuzzy vector-valued functions on time scales, Fuzzy Sets and Syst., 375 (2019), 1-52. doi: 10.1016/j.fss.2018.12.008. Google Scholar
[40]	C. Wang, R. P. Agarwal and D. O'Regan, $\Pi$-semigroup for invariant under translations time scales and abstract weighted pseudo almost periodic functions with applications, Dyna. Syst. Appl., 25 (2016), 1-28. Google Scholar
[41]	C. Wang, R. P. Agarwal and R. Sakthivel, Almost periodic oscillations for delay impulsive stochastic Nicholson's blowflies timescale model, Comput. Appl. Math., 37 (2018), 3005-3026. doi: 10.1007/s40314-017-0495-0. Google Scholar
[42]	C. Wang, G. Qin, R. P. Agarwal and D. O'Regan, $\Diamond_{\alpha}$-Measurability and combined measure theory on time scales, Applic. Anal., 2020. doi: 10.1080/00036811.2020.1820997. Google Scholar
[43]	C. Wang, R. P. Agarwal and D. O'Regan, $n_0$-order $\Delta$-almost periodic functions and dynamic equations, Applic. Anal., 97 (2018), 2626-2654. doi: 10.1080/00036811.2017.1382689. Google Scholar
[44]	C. Wang, R. P. Agarwal, D. O'Regan and R. Sakthivel, Theory of Translation Closedness for Time Scales, , Springer, Developments in Mathematics Series, Volume 62, Switzerland, 2020. doi: 10.1007/978-3-030-38644-3. Google Scholar
[45]	C. Wang and R. P. Agarwal, Almost periodic solution for a new type of neutral impulsive stochastic Lasota-Wazewska timescale model, Appl. Math. Lett., 70 (2017), 58-65. doi: 10.1016/j.aml.2017.03.009. Google Scholar
[46]	C. Wang and R. P. Agarwal, Almost automorphic functions on semigroups induced by complete-closed time scales and application to dynamic equations, Discrt. Contin. Dynam. Syst. B, 25 (2020), 781-798. doi: 10.3934/dcdsb.2019267. Google Scholar
[47]	J. Wang, M. Fěckan and Y. Zhou, Ulam's type stability of impulsive ordinary differential equations, J. Math. Anal. Appl., 395 (2012), 258-264. doi: 10.1016/j.jmaa.2012.05.040. Google Scholar
[48]	X. X. Hu and K. I. Kou, Quaternion Fourier and linear canonical inversion theorems, Math. Meth. Appl. Sci., 40 (2017), 2421-2440. doi: 10.1002/mma.4148. Google Scholar
[49]	Y. Xia, C. Jahanchahi and D. P. Mandic, Quaternion-valued echo state networks, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 663-673. doi: 10.1109/TNNLS.2014.2320715. Google Scholar
[50]	Z. P. Yang, T. Z. Xu and M. Qi, Ulam-Hyers stability for fractional differential equations in quaternionic analysis, Adv. Appl. Clifford Algebras, 26 (2016), 469-478. doi: 10.1007/s00006-015-0576-3. Google Scholar
[51]	Z. P. Yang, T. Z. Xu and M. Qi, The Cauchy problem for quaternion fuzzy fractional differential equations, J. Intelligent & Fuzzy Syst., 29 (2015), 451-461. doi: 10.3233/IFS-151612. Google Scholar

[1]	Golamreza Zamani Eskandani, Hamid Vaezi. Hyers--Ulam--Rassias stability of derivations in proper Jordan $CQ^{}$-algebras. Discrete & Continuous Dynamical Systems*, 2011, 31 (4) : 1469-1477. doi: 10.3934/dcds.2011.31.1469
[2]	Sung Kyu Choi, Namjip Koo. Stability of linear dynamic equations on time scales. Conference Publications, 2009, 2009 (Special) : 161-170. doi: 10.3934/proc.2009.2009.161
[3]	Yi Guan, Michal Fečkan, Jinrong Wang. Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows. Discrete & Continuous Dynamical Systems, 2021, 41 (3) : 1157-1176. doi: 10.3934/dcds.2020313
[4]	Ruichao Guo, Yong Li, Jiamin Xing, Xue Yang. Existence of periodic solutions of dynamic equations on time scales by averaging. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 959-971. doi: 10.3934/dcdss.2017050
[5]	Raegan Higgins. Asymptotic behavior of second-order nonlinear dynamic equations on time scales. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 609-622. doi: 10.3934/dcdsb.2010.13.609
[6]	B. Kaymakcalan, R. Mert, A. Zafer. Asymptotic equivalence of dynamic systems on time scales. Conference Publications, 2007, 2007 (Special) : 558-567. doi: 10.3934/proc.2007.2007.558
[7]	Saroj Panigrahi. Liapunov-type integral inequalities for higher order dynamic equations on time scales. Conference Publications, 2013, 2013 (special) : 629-641. doi: 10.3934/proc.2013.2013.629
[8]	Y. Gong, X. Xiang. A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales. Journal of Industrial & Management Optimization, 2009, 5 (1) : 1-10. doi: 10.3934/jimo.2009.5.1
[9]	Chao Wang, Ravi P Agarwal. Almost automorphic functions on semigroups induced by complete-closed time scales and application to dynamic equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 781-798. doi: 10.3934/dcdsb.2019267
[10]	Yongkun Li, Pan Wang. Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 463-473. doi: 10.3934/dcdss.2017022
[11]	Yunfei Peng, X. Xiang. A class of nonlinear impulsive differential equation and optimal controls on time scales. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1137-1155. doi: 10.3934/dcdsb.2011.16.1137
[12]	Yunfei Peng, X. Xiang, W. Wei. Backward problems of nonlinear dynamical equations on time scales. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1553-1564. doi: 10.3934/dcdss.2011.4.1553
[13]	Yung Chung Wang, Jenn Shing Wang, Fu Hsiang Tsai. Analysis of discrete-time space priority queue with fuzzy threshold. Journal of Industrial & Management Optimization, 2009, 5 (3) : 467-479. doi: 10.3934/jimo.2009.5.467
[14]	Giovanni Russo, Fabian Wirth. Matrix measures, stability and contraction theory for dynamical systems on time scales. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021188
[15]	Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200
[16]	Agnieszka B. Malinowska, Delfim F. M. Torres. Euler-Lagrange equations for composition functionals in calculus of variations on time scales. Discrete & Continuous Dynamical Systems, 2011, 29 (2) : 577-593. doi: 10.3934/dcds.2011.29.577
[17]	Christian Pötzsche, Stefan Siegmund, Fabian Wirth. A spectral characterization of exponential stability for linear time-invariant systems on time scales. Discrete & Continuous Dynamical Systems, 2003, 9 (5) : 1223-1241. doi: 10.3934/dcds.2003.9.1223
[18]	Andreas Hiltebrand, Siddhartha Mishra. Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography. Networks & Heterogeneous Media, 2016, 11 (1) : 145-162. doi: 10.3934/nhm.2016.11.145
[19]	Demou Luo, Qiru Wang. Dynamic analysis on an almost periodic predator-prey system with impulsive effects and time delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3427-3453. doi: 10.3934/dcdsb.2020238
[20]	Gerard A. Maugin, Martine Rousseau. Prolegomena to studies on dynamic materials and their space-time homogenization. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1599-1608. doi: 10.3934/dcdss.2013.6.1599

American Institute of Mathematical Sciences

Hyers-Ulam-Rassias stability of high-dimensional quaternion impulsive fuzzy dynamic equations on time scales

References:

References:

Tools

Metrics

Other articles
by authors

Tools

Tools

Metrics

Other articles
by authors

American Institute of Mathematical Sciences

Hyers-Ulam-Rassias stability of high-dimensional quaternion impulsive fuzzy dynamic equations on time scales

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors