Existence results of mild solutions for nonlocal fractional delay integro-differential evolution equations via Caputo conformable fractional derivative-Reference-Cited by-同舟云学术

Existence results of mild solutions for nonlocal fractional delay integro-differential evolution equations via Caputo conformable fractional derivative

Published:2022 Issue:7 Volume:7 Page:11614-11634
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Rabhi Lahcene¹,Al Horani Mohammed²,Khalil Roshdi²

Affiliation:

1. Laboratory of Geometry, Analysis, Control and Applications, Dr Moulay Tahar University of Saida, B. P. 138, En-nasr, 20000 Saida, Algeria

2. Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

Abstract

<abstract><p>In this paper, we investigate the existence of mild solutions for nonlocal delay fractional Cauchy problem with Caputo conformable derivative in Banach spaces. We establish a representation of a mild solution using a fractional Laplace transform. The existence of such solutions is proved under certain conditions, using the Mönch fixed point theorem and a general version of Gronwall's inequality under weaker conditions in the sense of Kuratowski measure of non compactness. Applications illustrating our main abstract results and showing the applicability of the presented theory are also given.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference48 articles.

1. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006.

2. A. B. Malinowska, D. F. M. Torres, Introduction to the fractional calculus of variations, Imp. Coll. Press, London, 2012.

3. K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, New York, 1993.

4. I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA, 1999.

5. T. Abdeljawad, On conformable fractional calculus, Comput. Appl. Math., 279 (2015), 57–66. https://doi.org/10.1016/j.cam.2014.10.016

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Solutions of Second-Order Nonlinear Implicit ψ-Conformable Fractional Integro-Differential Equations with Nonlocal Fractional Integral Boundary Conditions in Banach Algebra;Symmetry;2024-08-23

2. Sufficient conditions for existence of mild solutions for nondensely defined conformable fractional evolution equations in Banach spaces;FILOMAT;2024

3. Nonlocal second order delay semilinear integro-differential time varying evolution equation with convex-power condensing operators;FILOMAT;2024

4. Chaotic behavior and generation theorems of conformable time and space partial differential equations in specific Lebesgue spaces;Journal of Elliptic and Parabolic Equations;2023-12-22