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Maximum Principles and Applications for Fractional Differential Equations with Operators Involving Mittag-Leffler Function

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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.

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Authors and Affiliations

  1. Department of Mathematics, Yarmouk University Irbid, Yarmouk, Jordan

    Mohammed Al-Refai

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  1. Mohammed Al-Refai
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Correspondence to Mohammed Al-Refai.

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Al-Refai, M. Maximum Principles and Applications for Fractional Differential Equations with Operators Involving Mittag-Leffler Function. Fract Calc Appl Anal 24, 1220–1230 (2021). https://doi.org/10.1515/fca-2021-0052

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  • DOI: https://doi.org/10.1515/fca-2021-0052

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