Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Non-Instantaneous Impulses in Banach Spaces

Authors : Abdelkrim SALİM, Mouffak BENCHOHRA, Jamal Eddine LAZREG, Johnny HENDERSON

Pages : 332-348

Doi:10.31197/atnaa.825294

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Publication Date : 2020-12-30

Article Type : Research Paper

Abstract :In the present article, we prove some results concerning the existence of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional derivative in Banach spaces. The results are based on fixed point theorems of Darbo and Monch associated with the technique of measure of noncompactness. An example is included to show the applicability of our results. .
Keywords : Implicit fractional differential equations, generalized Hilfer fractional derivative, initial value problem, measure of noncompactness, fixed point, non instantaneous impulses, Ulam stability