An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method

Rezvan Ghoochani-Shirvan, Jafar Saberi-Nadjafi and Morteza Gachpazan

International Journal of Differential Equations, 2018, vol. 2018, 1-10

Abstract:

An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM). The approximate solutions of these equations are calculated in the form of a finite series with easily computable terms. The analytic solution is represented by an infinite series. We state and prove a theorem regarding an integral equation with a weak kernel by using the fractional differential transform method. The result of the theorem will be used to solve a weakly singular Volterra integral equation later on.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:7237680

DOI: 10.1155/2018/7237680

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