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A new solution method for nonlinear fractional integro-differential equations
1. | Department of Mathematics, Mustafa Kemal University, 31000, Hatay, Turkey |
References:
[1] |
A. Arikoglu and I. Ozkol, Solution of fractional integro-differential equations by using fractional differential transform method, Chaos, Solitons & Fractals, 40 (2009), 521-529.
doi: 10.1016/j.chaos.2007.08.001. |
[2] |
R. L. Bagley and J. P. Torvik, On the fractional calculus model of viscoelastic behavior, Journal of Rheology, 30 (1986), 133-155.
doi: 10.1122/1.549887. |
[3] |
M. El-Gamel and A. Zayed, Sinc-Galerkin method for solving nonlinear boundary-value problems, Comput. Math. Appl., 48 (2004), 1285-1298.
doi: 10.1016/j.camwa.2004.10.021. |
[4] |
E. Hesameddini and E. Asadolahifard, Solving Systems of Linear Volterra Integro-Differential Equations by Using Sinc-Collocation Method, International Journal of Mathematical Engineering and Science, 2 (2013), 1-9. |
[5] |
L. Huang, X. F. Li, Y. Zhao and X. Y. Duan, Approximate solution of fractional integro-differential equations by Taylor expansion method, Computers & Mathematics with Applications, 62 (2011), 1127-1134.
doi: 10.1016/j.camwa.2011.03.037. |
[6] |
J. Lund and K. L. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Englewood Cliffs, 1992.
doi: 10.1137/1.9781611971637. |
[7] |
F. Mainardi, The fundamental solutions for the fractional diffusion-wave equation, Applied Mathematics Letters, 9 (1996), 23-28.
doi: 10.1016/0893-9659(96)00089-4. |
[8] |
A. Mohsen and M. El-Gamel, On the Galerkin and collocation methods for two-point boundary value problems using sinc bases, Computers & Mathematics with Applications, 56 (2008), 930-941.
doi: 10.1016/j.camwa.2008.01.023. |
[9] |
A. Mohsen and M. El-Gamel, Sinc-collocation algorithm for solving nonlinear fredholm integro-differential equations, British Journal of Mathematics & Computer Science, 4 (2014), 1693-1700.
doi: 10.9734/BJMCS/2014/8247. |
[10] |
A. Mohsen and M. El-Gamel, A Sinc-Collocation method for the linear Fredholm integro-differential equations, Zeitschrift für angewandte Mathematik und Physik, 58 (2007), 380-390.
doi: 10.1007/s00033-006-5124-5. |
[11] |
S. Momani and M. A. Noor, Numerical methods for fourth-order fractional integro-differential equations, Applied Mathematics and Computation, 182 (2006), 754-760.
doi: 10.1016/j.amc.2006.04.041. |
[12] |
S. Momani and R. Qaralleh, An efficient method for solving systems of fractional integro-differentialequations, Computers & Mathematics with Applications, 52 (2006), 459-470.
doi: 10.1016/j.camwa.2006.02.011. |
[13] |
Y. Nawaz, Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations, Computers & Mathematics with Applications, 61 (2011), 2330-2341.
doi: 10.1016/j.camwa.2010.10.004. |
[14] |
D. Nazari and S. Shahmorad, Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions, Journal of Computational and Applied Mathematics, 234 (2010), 883-891.
doi: 10.1016/j.cam.2010.01.053. |
[15] |
I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999. |
[16] |
J. Rashidinia and M. Nabati, Sinc-Galerkin and Sinc-Collocation methods in the solution of nonlinear two-point boundary value problems, Computational and Applied Mathematics, 32 (2013), 315-330.
doi: 10.1007/s40314-013-0021-y. |
[17] |
F. Riewe, Mechanics with fractional derivatives, Physical Review E, 55 (1997), 3581-3592.
doi: 10.1103/PhysRevE.55.3581. |
[18] |
J. Sabatier, O. P. Agrawal and J. T. Machado, Advances in Fractional Calculus, Springer, Dordrecht, 2007.
doi: 10.1007/978-1-4020-6042-7. |
[19] |
R. K. Saedd and H. M. Sdeq, Solving a system of linear fredholm fractional integro-differential equations using homotopy perturbation method, Australian Journal of Basic and Applied Sciences, 4 (2010), 633-638. |
[20] |
A. Secer, S. Alkan, M. A. Akinlar and M. Bayram, Sinc-Galerkin method for approximate solutions of fractional order boundary value problems, Boundary Value Problems, 2013 (2013), 281-294. |
[21] |
M. Zarebnia and N. Zeinab, Solution of linear Volterra integro-differential equations via Sinc functions, International Journal of Applied Mathematics and Computation, 2 (2009), 1-10. |
[22] |
M. Zarebnia and M. G. A. Abadi, Numerical solution of system of nonlinear second-order integro-differential equations, Computers & Mathematics with Applications, 60 (2010), 591-601.
doi: 10.1016/j.camwa.2010.05.005. |
show all references
References:
[1] |
A. Arikoglu and I. Ozkol, Solution of fractional integro-differential equations by using fractional differential transform method, Chaos, Solitons & Fractals, 40 (2009), 521-529.
doi: 10.1016/j.chaos.2007.08.001. |
[2] |
R. L. Bagley and J. P. Torvik, On the fractional calculus model of viscoelastic behavior, Journal of Rheology, 30 (1986), 133-155.
doi: 10.1122/1.549887. |
[3] |
M. El-Gamel and A. Zayed, Sinc-Galerkin method for solving nonlinear boundary-value problems, Comput. Math. Appl., 48 (2004), 1285-1298.
doi: 10.1016/j.camwa.2004.10.021. |
[4] |
E. Hesameddini and E. Asadolahifard, Solving Systems of Linear Volterra Integro-Differential Equations by Using Sinc-Collocation Method, International Journal of Mathematical Engineering and Science, 2 (2013), 1-9. |
[5] |
L. Huang, X. F. Li, Y. Zhao and X. Y. Duan, Approximate solution of fractional integro-differential equations by Taylor expansion method, Computers & Mathematics with Applications, 62 (2011), 1127-1134.
doi: 10.1016/j.camwa.2011.03.037. |
[6] |
J. Lund and K. L. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Englewood Cliffs, 1992.
doi: 10.1137/1.9781611971637. |
[7] |
F. Mainardi, The fundamental solutions for the fractional diffusion-wave equation, Applied Mathematics Letters, 9 (1996), 23-28.
doi: 10.1016/0893-9659(96)00089-4. |
[8] |
A. Mohsen and M. El-Gamel, On the Galerkin and collocation methods for two-point boundary value problems using sinc bases, Computers & Mathematics with Applications, 56 (2008), 930-941.
doi: 10.1016/j.camwa.2008.01.023. |
[9] |
A. Mohsen and M. El-Gamel, Sinc-collocation algorithm for solving nonlinear fredholm integro-differential equations, British Journal of Mathematics & Computer Science, 4 (2014), 1693-1700.
doi: 10.9734/BJMCS/2014/8247. |
[10] |
A. Mohsen and M. El-Gamel, A Sinc-Collocation method for the linear Fredholm integro-differential equations, Zeitschrift für angewandte Mathematik und Physik, 58 (2007), 380-390.
doi: 10.1007/s00033-006-5124-5. |
[11] |
S. Momani and M. A. Noor, Numerical methods for fourth-order fractional integro-differential equations, Applied Mathematics and Computation, 182 (2006), 754-760.
doi: 10.1016/j.amc.2006.04.041. |
[12] |
S. Momani and R. Qaralleh, An efficient method for solving systems of fractional integro-differentialequations, Computers & Mathematics with Applications, 52 (2006), 459-470.
doi: 10.1016/j.camwa.2006.02.011. |
[13] |
Y. Nawaz, Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations, Computers & Mathematics with Applications, 61 (2011), 2330-2341.
doi: 10.1016/j.camwa.2010.10.004. |
[14] |
D. Nazari and S. Shahmorad, Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions, Journal of Computational and Applied Mathematics, 234 (2010), 883-891.
doi: 10.1016/j.cam.2010.01.053. |
[15] |
I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999. |
[16] |
J. Rashidinia and M. Nabati, Sinc-Galerkin and Sinc-Collocation methods in the solution of nonlinear two-point boundary value problems, Computational and Applied Mathematics, 32 (2013), 315-330.
doi: 10.1007/s40314-013-0021-y. |
[17] |
F. Riewe, Mechanics with fractional derivatives, Physical Review E, 55 (1997), 3581-3592.
doi: 10.1103/PhysRevE.55.3581. |
[18] |
J. Sabatier, O. P. Agrawal and J. T. Machado, Advances in Fractional Calculus, Springer, Dordrecht, 2007.
doi: 10.1007/978-1-4020-6042-7. |
[19] |
R. K. Saedd and H. M. Sdeq, Solving a system of linear fredholm fractional integro-differential equations using homotopy perturbation method, Australian Journal of Basic and Applied Sciences, 4 (2010), 633-638. |
[20] |
A. Secer, S. Alkan, M. A. Akinlar and M. Bayram, Sinc-Galerkin method for approximate solutions of fractional order boundary value problems, Boundary Value Problems, 2013 (2013), 281-294. |
[21] |
M. Zarebnia and N. Zeinab, Solution of linear Volterra integro-differential equations via Sinc functions, International Journal of Applied Mathematics and Computation, 2 (2009), 1-10. |
[22] |
M. Zarebnia and M. G. A. Abadi, Numerical solution of system of nonlinear second-order integro-differential equations, Computers & Mathematics with Applications, 60 (2010), 591-601.
doi: 10.1016/j.camwa.2010.05.005. |
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