Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ-Caputo Derivative in Banach and Fréchet Spaces
Joint Authors
Derbazi, Choukri
Baitiche, Zidane
N’Guérékata, G.
Benchohra, Mouffak
Source
International Journal of Differential Equations
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-10-14
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
Our aim in this paper is to investigate the existence, uniqueness, and Mittag–Leffler–Ulam stability results for a Cauchy problem involving ψ-Caputo fractional derivative with positive constant coefficient in Banach and Fréchet Spaces.
The techniques used are a variety of tools for functional analysis.
More specifically, we apply Weissinger’s fixed point theorem and Banach contraction principle with respect to the Chebyshev and Bielecki norms to obtain the uniqueness of solution on bounded and unbounded domains in a Banach space.
However, a new fixed point theorem with respect to Meir–Keeler condensing operators combined with the technique of Hausdorff measure of noncompactness is used to investigate the existence of a solution in Banach spaces.
After that, by means of new generalizations of Grönwall’s inequality, the Mittag–Leffler–Ulam stability of the proposed problem is studied on a compact interval.
Meanwhile, an extension of the well-known Darbo’s fixed point theorem in Fréchet spaces associated with the concept of measures of noncompactness is applied to obtain the existence results for the problem at hand.
Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility of the main theorems.
American Psychological Association (APA)
Derbazi, Choukri& Baitiche, Zidane& Benchohra, Mouffak& N’Guérékata, G.. 2020. Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ-Caputo Derivative in Banach and Fréchet Spaces. International Journal of Differential Equations،Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1169958
Modern Language Association (MLA)
Derbazi, Choukri…[et al.]. Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ-Caputo Derivative in Banach and Fréchet Spaces. International Journal of Differential Equations No. 2020 (2020), pp.1-16.
https://search.emarefa.net/detail/BIM-1169958
American Medical Association (AMA)
Derbazi, Choukri& Baitiche, Zidane& Benchohra, Mouffak& N’Guérékata, G.. Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ-Caputo Derivative in Banach and Fréchet Spaces. International Journal of Differential Equations. 2020. Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1169958
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1169958