Geodesic
Laplace Transform and Homotopy Perturbation Methods for Solving the Pseudohyperbolic Integrodifferential Problems with Purely Integral Conditions
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 251 .

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In this paper we defined and investigated the various properties of a class of pseudohyperbolic equation defined on purely integral (nonlocal) conditions. We proved the uniqueness and the existence of the solution using energy inequality (A priori estimates). We found a semi analytical solution using the Laplace transform and Stehfest algorithm method. Next, we used another method called the Homotopy perturbation. Finally, we give some examples for illustration.
Classification : 05C38, 15A15, 05A15, 15A18
Keywords: pseudohyperbolic integrodifferential equation, a priori estimate, Laplace transform method, Stehfest algorithm, homotopy perturbation method 
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     author = {A. Necib and A. Merad},
     title = {Laplace {Transform} and {Homotopy} {Perturbation} {Methods} for {Solving} the {Pseudohyperbolic} {Integrodifferential} {Problems} with {Purely} {Integral} {Conditions}},
     journal = {Kragujevac Journal of Mathematics},
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A. Necib; A. Merad. Laplace Transform and Homotopy Perturbation Methods for Solving the Pseudohyperbolic Integrodifferential Problems with Purely Integral Conditions. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 251 . http://geodesic.mathdoc.fr/item/KJM_2020_44_2_a6/