DÉRIVATION FRACTIONNAIRE APPLIQUÉE À L’ÉTUDE DE DEUX PROBLÈMES DIFFÉRENTIELS FRACTIONNAIRES NON-LINÉAIRES
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Abstract
The principle of fractional derivation has many applications. It intervenes in
the resolution of several nonlinear fractional problems in particular, in the
study of existence and uniqueness.
This paper discusses different appliquations of this principle as well as some
of its extensions and generalizations that involve in the resolution of nonlinear
fractional differential problems.We demonstrate the existence and uniqueness
of solutions using the principle of Banach contactions and the fixed point
theorems of Schaefer and Kranoselskii.
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Keywords
Equation différentielle fractionnaire non linéaire, problème aux limites,dérivée fractionnaire de Riemann, dérivée fractionnaire de Caputo, dérivée fractionnaire de Grunwald-Letnikov, intégrale fractionnaire de Riemann-Liouville,théorie du point fixe., Nonlinear fractional differential equation,boundary condition problem, Riemann fractional derivative,Caputo fractional derivative,fractional derivative of Grunwald-Letnikov,fractional integral of Riemann-Liouville, fixed-point theory.