1. Arikoglu, A. and Ozkol, I. Solution of fractional integro-differential equations by using fractional differential transform method, Chaos Solitons Fractals 40 (2009), 521–529.
2. Aslefallah, M. and Rostamy, D. A numerical scheme for solving space fractional equation by finite differences theta-method, Int. J. Adv. Appl. Math. Mech. 1 (4) (2014), 1–9.
3. Aslefallah, M., Rostamy, D., and Hosseinkhani, K. Solving time fractional differential diffusion equation by theta-method, Int. J. Adv. Appl. Math. Mech. 2 (1) (2014), 1–8.
4. Babolian, E., Maleknejad, K., and Mordad, M. A numerical method for solving Fredholm-Volterra integral equations in two-dimensional spaces using block pulse functions and an operational matrix, J. Comput. Appl. Math. 235 (14) (2011), 3965–3971.
5. Bahmanpour, M., Tavassoli Kajani, M., and Maleki, M. Solving Fred holm integral equations of the first kind using M¨untz wavelets, Appl. Numer. Math. 143 (2019), 159–171.
6. Biazar, J., and Ebrahimi, H. Chebyshev wavelets approach for non-linear systems of Volterra integral equations, Comput. Math. with Appl. 63(2012), 608–616.
7. Ebadian, A. and Khajehnasiri, A.A. Block-pulse functions and their applications to solving systems of higher-order nonlinear Volterra integro differential equations, Electron. J. Differ. Equ. 54 (2014), 1–9.
8. Esmaeili, S., Shamsi, M., and Luchko, Y. Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials, Comput. Math. Appl. 62(3) (2011), 918–929.
9. Hashim, I. Adomian decomposition method for solving BVPs for fourth order integro-differential equations, J. Comput. Appl. Math. 193 (2006), 658–64.
10. He, J.H. Approximation analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng. 167 (1988), 57–68.
11. Hilfer, R. Applications of fractional calculus in physics, World Scientific, Singapore, 2000.
12. Huang, L., Li, X.F., and Zhao, Y.L. Approximate solution of fractional integro-differential equations by Taylor expansion method, Comput. Math. Appl. 62 (2011), 1127–1134.
13. Keshavarz, E., Ordokhani, Y., and Razzaghi, M. Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations, Appl. Math. Model. 38 (2014), 6038–6051.
14. Khader, M.M. Numerical treatment for solving fractional Riccati differential equations, J. Egypt Math. Soc. 21 (2013), 32–37.
15. Li, Y.L. and Sun, N. Numerical solution of fractional differential equations using the generalized block pulse operational matrix, Comput. Math. Appl. 62 (2011), 1046–1054.
16. Ma, X.H. and Huang, C.M. Spectral collocation method for linear fractional integro-differential equations, Appl. Math. Model. 38 (2014), 1434–1448.
17. Meerschaert, M.M., Benson, D.A., and Bäumer, B. Multidimensional advection and fractional dispersion, Phys. Rev. E 59 (1999), 5026–5028.
18. Mittal, R.C. and Nigam, R. Solution of fractional calculus and fractional integro-differential equations by Adomian decomposition method, Int. J. Appl. Math. Mech. 4 (2) (2008), 87–94.
19. Mokhtary, P. and Ghoreishi, F. The L2-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integrodifferential equations, Numer. Algorithms 58 (2011), 475–496.
20. Mokhtary, P., Ghoreishi, F., and Srivastava, H.M. The Mu ¨ntz-Legendre Tau method for fractional differential equations, Appl. Math. Model. 40(2016), 671–684.
21. Nadzharyan, T.A., Sorokin, V.V., and Stepanov, G.V. A fractional calculus approach to modeling rheological behavior of soft magnetic elastomers, Polymer 92 (2010), 179–188.
22. Nawaz, Y. Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations, Comput. Math. Appl. 61 (2011), 2330–2341.
23. Nazari, D.and Shahmorad, S. Application of the fractional differential transform method to fractional order integro-defferential equations with nonlocal boundary conditions, J. Comput. Appl. Math. 234 (3) (2010), 883–891.
24. Pinkus, A. Density in approximation theory, Surv. Approx. Theory 1(2005), 1–45.
25. Podlubny, I. Fractional differential equation, Academic Press, San Diego, 1999.
26. Rana, S., Bhattacharya, S., and Pal, J. Paradox of enrichment: A fractional differential approach with memory, Phys. A Stat. Mech. Appl. 392 (2013), 3610–3621.
27. Sayevand, K., Fardi, M., and Moradi, E. Convergence analysis of homotopy perturbation method for Volterra integro-differential equations of fractional order, Alex. Eng. J. 52 (2013), 807–812.
28. Sutulo, S. and Soares, C.G. On applicability of mathematical models based on fractional calculus to ship dynamics, in: Proceedings of the Conference on Control Applications in Marine Systems (2010), 15–17.
29. Sweilam, N.H., Khader, M.M., and Al-Bar, R.F. Numerical studies for a multi-order fractional differential equation, Phys. Lett. A. 371 (2007)26–33.
30. Wang, J., Xu, T., Wei, Y., and Xie, J. Numerical simulation for coupled systems of nonlinear fractional order integro-differential equations viawavelets method, Appl. Math. Comput. 324 (2018), 36–50.
31. Wang, L.F., Ma, Y.P., and Meng, Z.J. Haar wavelet method for solving fractional partial differential equations numerically, Appl. Math. Comput. 227 (2014), 66–76
32. Xie, J., Huang, Q., and Zhao, F. Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations in two-dimensional spaces based on Block Pulse functions, J J. Comput. Appl. Math. 317(2017), 565–572.
33. Xie, J. and Yi, M. Numerical research of nonlinear system of fractional Volterra-Fredholm integral-differential equations via Block-Pulse functions and error analysis, J. Comput. Appl. Math. 345 (2019), 159–167.
34. Yang, Y., Chen, Y.P., and Huang, Y.Q. Convergence analysis of the Jacobi spectral-collocation method for fractional integro-differential equations, Acta Mathematica Scientia 34B (3) (2014), 673–690.
35. Yi, M.X., Wang, L.F., and Huang, J. Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel, Appl. Math. Model. 40 (2016), 3422–3437.
36. Zhang, X.D., Tang, B., and He, Y.N. Homotopy analysis method for higher-order fractional integro-differential equations, Comput. Math. Appl. 62 (2011), 3194–3203.
37. Zhu, L. and Fan, Q.B. Solving fractional nonlinear Fredholm integro differential equations by the second kind Chebyshev wavelets, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 2333–2341.
Send comment about this article