Geodesic
Existence and uniqueness of the solution for Volterra--Fredholm integro-differential equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 692-701

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In this article, modified Adomian decomposition method is successfully applies to find the approximate solutions of Volterra–Fredholm integro-differential equations. Moreover, we prove the existence and uniqueness results and convergence of the solutions. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.
Keywords: Modified Adomian decomposition method, Volterra–Fredholm integro-differential equation, existence and uniqueness results, approximate solution. 
@article{JSFU_2018_11_6_a4,
     author = {Ahmed A. Hamoud and Kirtiwant P. Ghadle},
     title = {Existence and uniqueness of the solution for {Volterra--Fredholm} integro-differential equations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {692--701},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a4/}
}
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Ahmed A. Hamoud; Kirtiwant P. Ghadle. Existence and uniqueness of the solution for Volterra--Fredholm integro-differential equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 692-701. http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a4/