Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind-Reference-Cited by-同舟云学术

Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind

Published:2013 Issue: Volume:2013 Page:1-11
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Atangana Abdon¹^ORCID,Bildik Necdet²^ORCID

Affiliation:

1. Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa

2. Department of Mathematics, Faculty of Art & Sciences, Celal Bayar University, Muradiye Campus, 45047 Manisa, Turkey

Abstract

This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2013/981526.pdf

Reference34 articles.

1. Numerical solution of non-linear Fredholm integral equations by using multiwavelets in the Petrov–Galerkin method

2. Analytical Solutions of the Space-Time Fractional Derivative of Advection Dispersion Equation

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