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

Yıl 2023, Cilt: 7 Sayı: 1, 1 - 28, 31.03.2023

Soumıa Bourchi , Fahd Jarad , Yassine Adjabı , Thabet Abdeljawad , Ibrahim Mahariq

https://doi.org/10.31197/atnaa.1147950

Öz

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

Anahtar Kelimeler

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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