Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function-Reference-Cited by-同舟云学术

Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function

Published:2021-08-01 Issue:4 Volume:24 Page:1220-1230
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Al-Refai Mohammed¹

Affiliation:

1. Department of Mathematics Yarmouk University Irbid , Yarmouk Jordan

Abstract

Abstract In this paper, we formulate and prove two maximum principles to nonlinear fractional differential equations. We consider a fractional derivative operator with Mittag-Leffler function of two parameters in the kernel. These maximum principles are used to establish a pre-norm estimate of solutions, and to derive certain uniqueness and positivity results to related linear and nonlinear fractional initial value problems.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2021-0052/pdf

Reference18 articles.

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2. M. Al-Refai, Yu. Luchko, Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives. J. Appl. Math. and Computation 257 (2015), 40–51.

3. M. Al-Refai, Yu. Luchko, Analysis of fractional diffusion equations of distributed order: Maximum principles and their applications. Analysis 36, No 2 (2015); DOI: 10.1515/anly-2015-5011.

4. M. Al-Refai, Maximum principles for nonlinear fractional differential equations in reliable space. Progress in Fract. Differentiation and Appl. 6, No 2 (2020), 95–99.

5. R. Gorenflo, A. Kilbas, F. Mainardi, S. Rogosin, Mittag-Leffler Functions, Related Topics and Applications: Theory and Applications. Springer-Verlag, Berlin-Heidelberg, 2014; 2nd Ed. 2020.

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