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

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 th...

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Bibliographic Details
Main Authors: Soumia Bourchi, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad, Ibrahim Mahariq
Format: Article
Language:English
Published: ATNAA 2023-03-01
Series:Advances in the Theory of Nonlinear Analysis and its Applications
Subjects:
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
Online Access:https://atnaea.org/index.php/journal/article/view/1/8
Description
Summary: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
ISSN:2587-2648

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