J. Nonl. Evol. Equ. Appl. 2018 (3), pp. 27-37, published on August 22, 2019:

Analytical Solution of Linear Integro-Differential Equations with Weakly Singular Kernel by Using Taylor Expansion Method

K. Fernane

Department of Mathematics, Laboratory of Applied Mathematics and Modeling,
University of 8 May 1945 Guelma Algeria.

Received on July 9, 2017, revised version February 21, 2018
Accepted on February 23, 2018

Communicated by Ti-Jun Xiao

Abstract.  In this paper, we apply Taylor's approximation and then transform the given n-th order weakly singular linear Volterra and Fredholm integro-differential equations with into an ordinary linear differential equation.Some different examples are considered, the results of these examples indicated that the procedure of transformation method is simple and effective and could provide an accurate approximate solution or exact solution.
Keywords:General Abel Integral, Integro-differential Equations, Weakly singular Fredholm integral-equations, Weakly singular Volterra integral-equations,Taylor’s series approximation..
2010 Mathematics Subject Classification:   45A05, 32A55, 34A25, 65T60.

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