Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space

Author:

Mohan Raja Marimuthu1,Vijayakumar Velusamy1ORCID,Shukla Anurag2,Nisar Kottakkaran Sooppy3,Rezapour Shahram45

Affiliation:

1. Department of Mathematics , School of Advanced Sciences, Vellore Institute of Technology , Vellore 632 014 , Tamilnadu , India

2. Department of Applied Science , Rajkiya Engineering College Kannauj , Kannauj 209732 , India

3. Department of Mathematics , College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991 , Saudi Arabia

4. Department of Mathematics , Azarbaijan Shahid Madani University , Tabriz , Iran

5. Department of Medical Research , China Medical University Hospital, China Medical University , Taichung , Taiwan, ROC

Abstract

Abstract This manuscript investigates the issue of existence results for fractional differential evolution inclusions of order r ∈ (1, 2) in the Banach space. In the beginning, we analyze the existence results by referring to the fractional calculations, cosine families, multivalued function, and Martelli’s fixed point theorem. The result is also used to investigate the existence of nonlocal fractional evolution inclusions of order r ∈ (1, 2). Finally, a concrete application is given to illustrate our main results.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Reference48 articles.

1. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam, Elsevier, 2006.

2. V. Lakshmikantham, S. Leela, and J. V. Devi, Theory of Fractional Dynamic Systems, Cambridge, Cambridge Scientific Publishers, 2009.

3. I. Podlubny, Fractional Differential Equations, an Introduction to Fractional Derivatives, Fractional Differential Equations, to Method of Their Solution and Some of Their Applications, San Diego, CA, Academic Press, 1999.

4. Y. Zhou, Basic Theory of Fractional Differential Equations, Singapore, World Scientific, 2014.

5. Y. Zhou, Fractional Evolution Equations and Inclusions: Analysis and Control, New York, Elsevier, 2015.

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