On abstract Cauchy problems in the frame of a generalized Caputo type derivative

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:7 Issue:1
On abstract Cauchy problems in the frame of a generalized Caputo type derivative

On abstract Cauchy problems in the frame of a generalized Caputo type derivative

Authors : Soumıa BOURCHİ, Fahd JARAD, Yassine ADJABI, Thabet ABDELJAWAD, Ibrahim MAHARİQ

Pages : 1-28

Doi:10.31197/atnaa.1147950

View : 344 | Download : 320

Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results
Keywords : Caputo type generalized fractional operators, abstract Cauchy problem, existence, uniqueness, continuous dependence on parameters, stability, uniformly continuous semigroups, fixed point theorems, Mittag Leffler type function

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