Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:4 Issue:4
Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces

Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces

Authors : Choukri DERBAZİ, Zidane BAİTİCHE, Mouﬀak BENCHOHRA

Pages : 349-360

Doi:10.31197/atnaa.706292

View : 17 | Download : 10

Publication Date : 2020-12-30

Article Type : Research Paper

Abstract :This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the $\psi $--Caputo fractional derivative in Banach spaces. Our approach is based on a new fixed point theorem with respect to convex-power condensing operator combined with the technique of measures of noncompactness. Finally, two examples are given to illustrate the obtained results.
Keywords : psi Caputo fractional derivative, Cauchy problem, convex power condensing operator, fixed point theorem, Banach spaces, measures of noncompactness

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