Boundary problems of fractional differential equations according to the Hadamard derivative and integralapproach. Theoretical and numerical aspects.
Boundary problems of fractional differential equations according to the Hadamard derivative and integralapproach. Theoretical and numerical aspects.
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Date
2021-12-06
Auteurs
DJERIBA Hichem
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Éditeur
Université Oran1 Ahmed Ben Bella
Résumé
The objective of this thesis is to search for solutions of fractional differential equations where we use Haddamard derivatives and presents the analytical solutions of the Fractional Burgers Kuramoto KdV equation and one-dimensional Fractional diffusion equations by the variational iteration method and Adomian's decomposition method. By using initial conditions, the explicit solutions of the Burgers Kuramoto Kdv equation and one-dimensional Fractional diffusion equations have been presented. The fractional derivatives are considered according to Hadamard's approach. Examples are given to illustrate the implementation of the variational iteration method and Adomian's decomposition method for fractional Burgers Kuramoto KdV equation and one-dimensional Fractional di usion equations.
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Mots-clés
Hadamard Derivatives, Fractional Calculus, Fractional Diffusion Equation, Fractional Burgers Kuramoto, Kdv Equation, Variational Iteration Method, Adomain's Decom-Position Method, Fractional Derivatives, Dimensional Fractional