Nonlinear Implicit Hadamard's Fractional Differential Equa- tions with Retarded and Advanced Arguments

Mouffak Benchohra, Soufyane Bouriah, Johnny Henderson

Abstract


In this paper, we establish the existence and uniqueness of solutions for a class of
problem for nonlinear implicit fractional dierential equations (NIFDE for short) of Hadamard type involving both retarded and advanced arguments. The proofs of our main results are based upon the Banach contraction principle and the Schauder xed point theorem. We present two examples to show the applicability of our results.


Keywords


Hadamard's fractional derivative, implicit fractional dierential equa- tions, fractional integral, existence, retarded arguments, advanced arguments, fixed point

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