Application of Shehu transform to Atangana-Baleanu derivatives

Volume 20, Issue 2, pp 101--107 http://dx.doi.org/10.22436/jmcs.020.02.03

Publication Date: October 19, 2019 Submission Date: April 05, 2019 Revision Date: September 07, 2019 Accteptance Date: September 10, 2019

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Authors

Ahmed Bokhari - Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Algeria. Dumitru Baleanu - Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, TR-06530 Ankara, Turkey. - Institute of Space Science, R-077125 Magurle-Bucharest, Romania. Rachid Belgacem - Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Algeria.

Abstract

Recently, Shehu Maitama and Weidong Zhao proposed a new integral transform, namely, Shehu transform, which generalizes both the Sumudu and Laplace integral transforms. In this paper, we present new further properties of this transform. We apply this transformation to Atangana--Baleanu derivatives in Caputo and in Riemann--Liouville senses to solve some fractional differential equations.

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Keywords

• Shehu transform
• Mittag-Leffler kernel
• non-singular and non-local fractional operators

MSC

•  26A33
•  65R10
•  34A08

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