Geodesic
The approximate solutions of fractional Volterra--Fredholm integro-differential equations by using analytical techniques
Problemy analiza, Tome 7 (2018) no. 1, pp. 41-58

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This paper demonstrates a study on some significant latest innovations in the approximation techniques to find the approximate solutions of Caputo fractional Volterra–Fredholm integro-differential equations. To apply this, the study uses Adomian decomposition method and modified Laplace Adomian decomposition method. A wider applicability of these techniques is based on their reliability and reduction in the size of the computational work. This study provides analytical approximate to determine the behavior of the solution. It proves the existence and uniqueness results and convergence of the solution. In addition, it brings an example to examine the validity and applicability of the proposed techniques.
Keywords: Adomian decomposition method; Laplace transform; Volterra–Fredholm integro-differential equation; Caputo fractional derivative. 
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     author = {A. A. Hamoud and K. P. Ghadle},
     title = {The approximate solutions of fractional {Volterra--Fredholm} integro-differential equations by using analytical techniques},
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A. A. Hamoud; K. P. Ghadle. The approximate solutions of fractional Volterra--Fredholm integro-differential equations by using analytical techniques. Problemy analiza, Tome 7 (2018) no. 1, pp. 41-58. http://geodesic.mathdoc.fr/item/PA_2018_7_1_a2/