Etude de certains problèmes d’équations différentielles fractionnaires
Etude de certains problèmes d’équations différentielles fractionnaires
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Date
2025-09-25
Auteurs
CHOHRI Mohamed
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Université Oran1
Résumé
In this Thesis, we employ Mawhin’s theory of degree of coincidence to study the existence and uniqueness result for a class of problem for nonlinear implicit fractional differential equations (NIFDE ) with Caputo’s exponential fractional derivative and for a class of problems involving non-linear implicit fractional differential equations with the exponentially fractional derivative of Caputo. Finally we are discussing the periodic solutions for the implicit problem with nonlinear fractional pantograph differential equation involving the Caputo tempered fractional derivative. The proofs are based upon the coincidence degree theory of Mawhin. Several enlightening examples are also presented to demonstrate the applicability of our results.
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Mots-clés
Caputo’s exponential fractional derivative; Tempered fractional operators; implicit fractional; fractional integral existence; periodic solutions; coincidence degree theory; differential equations.