International Journal of Differential Equations

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

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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.

Article information

Source
Int. J. Differ. Equ., Volume 2018 (2018), Article ID 7237680, 10 pages.

Dates
Received: 17 August 2017
Revised: 24 November 2017
Accepted: 18 January 2018
First available in Project Euclid: 8 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1525744831

Digital Object Identifier
doi:10.1155/2018/7237680

Mathematical Reviews number (MathSciNet)
MR3786318

Zentralblatt MATH identifier
06915960

Citation

Ghoochani-Shirvan, Rezvan; Saberi-Nadjafi, Jafar; Gachpazan, Morteza. An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method. Int. J. Differ. Equ. 2018 (2018), Article ID 7237680, 10 pages. doi:10.1155/2018/7237680. https://projecteuclid.org/euclid.ijde/1525744831


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