Abstract
Abstract
In this study, a wavelet method is developed to solve a system of nonlinear variable-order (V-O) fractional integral equations using the Chebyshev wavelets (CWs) and the Galerkin method. For this purpose, we derive a V-O fractional integration operational matrix (OM) for CWs and use it in our method. In the established scheme, we approximate the unknown functions by CWs with unknown coefficients and reduce the problem to an algebraic system. In this way, we simplify the computation of nonlinear terms by obtaining some new results for CWs. Finally, we demonstrate the applicability of the presented algorithm by solving a few numerical examples.
Funder
National Natural Science Foundation of China Project
Hunan Provincial Science and Technology Department
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference42 articles.
1. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
2. Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)
3. Hesameddini, E., Rahimi, A., Asadollahifard, E.: On the convergence of a new reliable algorithm for solving multi-order fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 34, 154–164 (2016)
4. Almeida, R., Torres, D.F.M.: An introduction to the fractional calculus and fractional differential equations. Sci. World J. 2013, Article ID 915437 (2013)
5. Zaky, M.A., Doha, E.H., Taha, T.M., Baleanu, D.: New recursive approximations for variable-order fractional operators with applications. Math. Model. Anal. 23, 227–239 (2018)
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献