Title : ( An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method )
Authors: Rezvan Ghoochani shirvan , Jafar Saberi- Nadjafi , Mortaza Gachpazan ,
Full TextAbstract
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 formof a finite series with easily computable terms.Theanalytic 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.
Keywords
, Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel, Fractional Differential Transform Method
@article{paperid:1067932,
author = {Ghoochani Shirvan, Rezvan and Saberi- Nadjafi, Jafar and Gachpazan, Mortaza},
title = {An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method},
journal = {International Journal of Differential Equations},
year = {2018},
volume = {2018},
number = {1},
month = {April},
issn = {1687-9643},
pages = {1--10},
numpages = {9},
keywords = {Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel; Fractional Differential
Transform Method},
}
%0 Journal Article
%T An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method
%A Ghoochani Shirvan, Rezvan
%A Saberi- Nadjafi, Jafar
%A Gachpazan, Mortaza
%J International Journal of Differential Equations
%@ 1687-9643
%D 2018
