• Previous Article
    Convex combination of data matrices: PCA perturbation bounds for multi-objective optimal design of mechanical metafilters
  • MFC Home
  • This Issue
  • Next Article
    On multidimensional Urysohn type generalized sampling operators
doi: 10.3934/mfc.2021004
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.

Iyengar-Hilfer fractional inequalities

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

Received  February 2021 Early access March 2021

Here we present Iyengar type integral inequalities. At the univariate level they involve $ \psi $-Hilfer left and right fractional derivatives. At the multivariate level they involve Hilfer left and right fractional derivatives, and they deal with radial and non-radial functions on the ball and spherical shell. All estimates are with respect to norms $ \left \Vert \cdot \right \Vert _{p} $, $ 1\leq p\leq \infty $. At the end we provide an application.

Citation: George A. Anastassiou. Iyengar-Hilfer fractional inequalities. Mathematical Foundations of Computing, doi: 10.3934/mfc.2021004
References:
[1]

R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simul., 44 (2017), 460-481.  doi: 10.1016/j.cnsns.2016.09.006.  Google Scholar

[2]

S. S. Dragomir, Inequalities for the Riemann-Stieljes integral of $\left( p,q\right) -H-$dominated integrators with applications, Appl. Math. E-Notes, 15 (2015), 243-260.   Google Scholar

[3]

K. S. K. Iyengar, Note on an inequality, Math. Stud., 6 (1938), 75-76.   Google Scholar

[4]

A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differentiation Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.  Google Scholar

[5]

W. Rudin, Real and Complex Analysis, McGraw-Hill Book Co., New York-Toronto, Ont. -London, 1966.  Google Scholar

[6]

S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, Yverdon, 1993.  Google Scholar

[7]

D. W. Stroock, A Concise Introduction to the Theory of Integration, Birkhaüser Boston, Inc, Boston, MA, 1999.  Google Scholar

[8]

Ž. TomovskiR. Hilfer and H. M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions, Integral Transforms Spec Funct., 21 (2010), 797-814.  doi: 10.1080/10652461003675737.  Google Scholar

[9]

J. Vanterler da C. Sousa and E. Capelas de Oliveira, On the $\psi $-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul., 60 (2018), 72-91.  doi: 10.1016/j.cnsns.2018.01.005.  Google Scholar

show all references

References:
[1]

R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simul., 44 (2017), 460-481.  doi: 10.1016/j.cnsns.2016.09.006.  Google Scholar

[2]

S. S. Dragomir, Inequalities for the Riemann-Stieljes integral of $\left( p,q\right) -H-$dominated integrators with applications, Appl. Math. E-Notes, 15 (2015), 243-260.   Google Scholar

[3]

K. S. K. Iyengar, Note on an inequality, Math. Stud., 6 (1938), 75-76.   Google Scholar

[4]

A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differentiation Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.  Google Scholar

[5]

W. Rudin, Real and Complex Analysis, McGraw-Hill Book Co., New York-Toronto, Ont. -London, 1966.  Google Scholar

[6]

S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, Yverdon, 1993.  Google Scholar

[7]

D. W. Stroock, A Concise Introduction to the Theory of Integration, Birkhaüser Boston, Inc, Boston, MA, 1999.  Google Scholar

[8]

Ž. TomovskiR. Hilfer and H. M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions, Integral Transforms Spec Funct., 21 (2010), 797-814.  doi: 10.1080/10652461003675737.  Google Scholar

[9]

J. Vanterler da C. Sousa and E. Capelas de Oliveira, On the $\psi $-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul., 60 (2018), 72-91.  doi: 10.1016/j.cnsns.2018.01.005.  Google Scholar

[1]

Pallavi Bedi, Anoop Kumar, Thabet Abdeljawad, Aziz Khan. S-asymptotically $ \omega $-periodic mild solutions and stability analysis of Hilfer fractional evolution equations. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020089

[2]

Yu-Ming Chu, Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Humaira Kalsoom. More new results on integral inequalities for generalized $ \mathcal{K} $-fractional conformable Integral operators. Discrete & Continuous Dynamical Systems - S, 2021, 14 (7) : 2119-2135. doi: 10.3934/dcdss.2021063

[3]

Beom-Seok Han, Kyeong-Hun Kim, Daehan Park. A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on $ C^{1} $ domains. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3415-3445. doi: 10.3934/dcds.2021002

[4]

Ekta Mittal, Sunil Joshi. Note on a $ k $-generalised fractional derivative. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 797-804. doi: 10.3934/dcdss.2020045

[5]

Yousef Alnafisah, Hamdy M. Ahmed. Neutral delay Hilfer fractional integrodifferential equations with fractional brownian motion. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021031

[6]

Fahd Jarad, Thabet Abdeljawad. Generalized fractional derivatives and Laplace transform. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 709-722. doi: 10.3934/dcdss.2020039

[7]

Ramasamy Subashini, Chokkalingam Ravichandran, Kasthurisamy Jothimani, Haci Mehmet Baskonus. Existence results of Hilfer integro-differential equations with fractional order. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 911-923. doi: 10.3934/dcdss.2020053

[8]

Saïd Abbas, Mouffak Benchohra, John R. Graef. Coupled systems of Hilfer fractional differential inclusions in banach spaces. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2479-2493. doi: 10.3934/cpaa.2018118

[9]

Fahd Jarad, Thabet Abdeljawad. Variational principles in the frame of certain generalized fractional derivatives. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 695-708. doi: 10.3934/dcdss.2020038

[10]

Shihu Li, Wei Liu, Yingchao Xie. Large deviations for stochastic 3D Leray-$ \alpha $ model with fractional dissipation. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2491-2509. doi: 10.3934/cpaa.2019113

[11]

Phuong Le. Symmetry of singular solutions for a weighted Choquard equation involving the fractional $ p $-Laplacian. Communications on Pure & Applied Analysis, 2020, 19 (1) : 527-539. doi: 10.3934/cpaa.2020026

[12]

Zaizheng Li, Qidi Zhang. Sub-solutions and a point-wise Hopf's lemma for fractional $ p $-Laplacian. Communications on Pure & Applied Analysis, 2021, 20 (2) : 835-865. doi: 10.3934/cpaa.2020293

[13]

Alessio Fiscella. Schrödinger–Kirchhoff–Hardy $ p $–fractional equations without the Ambrosetti–Rabinowitz condition. Discrete & Continuous Dynamical Systems - S, 2020, 13 (7) : 1993-2007. doi: 10.3934/dcdss.2020154

[14]

Harbir Antil, Mahamadi Warma. Optimal control of the coefficient for the regional fractional $p$-Laplace equation: Approximation and convergence. Mathematical Control & Related Fields, 2019, 9 (1) : 1-38. doi: 10.3934/mcrf.2019001

[15]

Yong Zhou, Jia Wei He. New results on controllability of fractional evolution systems with order $ \alpha\in (1,2) $. Evolution Equations & Control Theory, 2021, 10 (3) : 491-509. doi: 10.3934/eect.2020077

[16]

Elhoussine Azroul, Abdelmoujib Benkirane, and Mohammed Shimi. On a nonlocal problem involving the fractional $ p(x,.) $-Laplacian satisfying Cerami condition. Discrete & Continuous Dynamical Systems - S, 2021, 14 (10) : 3479-3495. doi: 10.3934/dcdss.2020425

[17]

Lihong Zhang, Wenwen Hou, Bashir Ahmad, Guotao Wang. Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian. Discrete & Continuous Dynamical Systems - S, 2021, 14 (10) : 3851-3863. doi: 10.3934/dcdss.2020445

[18]

Fahd Jarad, Sugumaran Harikrishnan, Kamal Shah, Kuppusamy Kanagarajan. Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 723-739. doi: 10.3934/dcdss.2020040

[19]

Claudianor O. Alves, Vincenzo Ambrosio, Teresa Isernia. Existence, multiplicity and concentration for a class of fractional $ p \& q $ Laplacian problems in $ \mathbb{R} ^{N} $. Communications on Pure & Applied Analysis, 2019, 18 (4) : 2009-2045. doi: 10.3934/cpaa.2019091

[20]

Lun Guo, Wentao Huang, Huifang Jia. Ground state solutions for the fractional Schrödinger-Poisson systems involving critical growth in $ \mathbb{R} ^{3} $. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1663-1693. doi: 10.3934/cpaa.2019079

 Impact Factor: 

Article outline

[Back to Top]