Abstract
In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal method in solving these problems.
Highlights
Fractional integro-differential equations (FIDE’s) occur in many applications in the sciences (1)
Mohamed et al (5) in 2016 introduced an analytical method, called homotopy analysis transform method (HATM) which is a combination of HAM and Laplace decomposition method, this scheme is applied to linear and nonlinear fractional integro-differential equations
This study aims to find numerical solutions of LFVFIDE of the following form: Dαu(x) = q(x) u(x) + f(x)
Summary
Fractional integro-differential equations (FIDE’s) occur in many applications in the sciences (physics, engineering, finance, biology) (1). In most of the problems the analytical solution cannot be found, and finding a good approximate solution using numerical methods will be very helpful (2). Mittal and Nigam (1) in 2014 used Adomian decomposition approach to find numerical solution to FIDE’s of Volterra type with Caputo fractional derivative. Huang et al (3) in 2011 used Taylor expansion series for solving (approximately) a class of linear fractional integrodifferential equations including two types Fredholm and Volterra. Maleknejad et al (4) in 2013 presented a numerical scheme, based on the cubic B-spline wavelets for solving fractional integrodifferential equations. Mohamed et al (5) in 2016 introduced an analytical method, called homotopy analysis transform method (HATM) which is a combination of HAM and Laplace decomposition method, this scheme is applied to linear and nonlinear fractional integro-differential equations
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