On fractional evolution equations with an extended ψ−fractional derivative-Reference-Cited by-同舟云学术

On fractional evolution equations with an extended ψ−fractional derivative

Published:2023 Issue:21 Volume:37 Page:7231-7240
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Oufkir Khadija¹,El Mfadel²,Melliani Said¹,Elomari Mhamed¹,Sadiki Hamid¹

Affiliation:

1. Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco

2. Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco + Superior School of Technology, Sultan Moulay Slimane University, Khénifra, Morocco

Abstract

This manuscript aims to highlight the existence and uniqueness results for a class of fuzzy nonlinear fractional evolution equations. Our approach is based on the application of an extended ??Caputo fractional derivative of order q ?(0,1) valid on fuzzy functions paired with Banach contraction principle. As an example of application, we provide one at the end of this paper to show how the results can be used.

Publisher

National Library of Serbia

Reference42 articles.

1. K. Abuasbeh, R. Shafqat, A.U.K. Niazi and M. Awadalla, Local and global existence and uniqueness of solution for class of fuzzy fractional functional evolution equation, Journal of Function Spaces, vol.2022, art.n.7512754, (2022)

2. R.P. Agarwal, M. Belmekki and M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative. Adv. Difference Equ. (2009).

3. R.P. Agarwal, V. Lakshmikantham and J.J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Analysis: Theory, Methods and Applications, (72), (2010), 2859 − 2862.

4. R. Alikhani and F. Bahrami, Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations, Commun Nonlinear Sci Numer Simulat (18), (2013), 2007 − 2017.

5. T. Allahviranloo, S. Salahshour, and S. Abbasbandy. Explicit solutions of fractional differential equations with uncertainty. Soft Computing, 16(2), (2012), 297-302.