Available online at www.isr-publications.com/jmcs J. Math. Computer Sci., 20 (2020), 101–107 Research Article Online: ISSN 2008-949X Journal Homepage: www.isr-publications.com/jmcs Application of Shehu transform to Atangana-Baleanu deriva- tives Ahmed Bokhari a , Dumitru Baleanu b,c,∗ , Rachid Belgacem a a Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Algeria. b Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, TR-06530 Ankara, Turkey. c Institute of Space Science, R-077125 M ˘ agurle-Bucharest, Romania. Abstract Recently, Shehu Maitama and Weidong Zhao proposed a new integral transform, namely, Shehu transform, which general- izes 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. Keywords: Shehu transform, Mittag-Leffler kernel, non-singular and non-local fractional operators. 2010 MSC: 26A33, 65R10, 34A08. c 2020 All rights reserved. 1. Introduction The resolution of fractional differential equations has become a fertile mathematical field, Many re- searches that give innovative methods, meet the needs of other sciences. the derivatives of Caputo and Riemann–Liouville were the most appropriate way to model the various natural phenomena, which re- quire non-integer derivatives, but its limitations in some respects led to the search for other deriva- tives. Both Caputo and Riemann–Liouville fractional derivatives have singular kernels. In addition, the Riemann–Liouville derivative of the constant does not equal zero. To overcome the disadvantage of the singular kernel, Caputo and Fabrizio [7] presented a fractional derivative operator without a singular kernel. Caputo-Fabrizio operator has proved to be effective through some applications [1, 12]. In [2], the authors proposed a genuine new fractional derivatives based on the Mittag-Leffler function. One is the ABR derivative (Riemann–Liouville sense), the other is the ABC derivative (Caputo sense). In addition to the fact that the kernel is non-singular and non-local, the ABC and ABR derivatives includes all the prop- erties of the fractional derivatives except the semigroup property. However, recently these new fractional operators were recognized in one recently established classification of fractional operators [16]. ∗ Corresponding author Email addresses: bokhari.ahmed@ymail.com (Ahmed Bokhari), dumitru.baleanu@gmail.com (Dumitru Baleanu), belgacemrachid02@yahoo.fr (Rachid Belgacem) doi: 10.22436/jmcs.020.02.03 Received: 2019-04-05 Revised: 2019-09-07 Accepted: 2019-09-10