Méthodes numériques pour la résolution des équations différentielles fractionnaires
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Date
2022
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Publisher
Université de M'sila
Abstract
The main objective of this thesis is to present the finite difference method to approximate fractional derivatives, in
order to find numerical solutions to linear fractional differentials equations and partial differentials equations,
involving Caputo-Hadamard and Caputo-Katugampola fractional derivative. As such, the convergence and
stability of the numerical schemes are proved using mathematical induction. illustrative examples have been
presented to show the effectiveness and validity of our method
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Keywords
Fractional differential equations, Finite difference methods, Caputo-Hadamard fractional derivative, Caputo-Katugampola derivative, Convergence, Stability