Browsing by Author "Belgacem, Rachid"

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Application of Shehu Transform To Atangana-Baleanu Derivatives
(int Scientific Research Publications, 2020) Bokhari, Ahmed; Baleanu, Dumitru; Baleanu, Dumitru; Belgacem, Rachid; 56389
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.
Projectile motion using three parameter Mittag-Leffler function calculus
(Elsevier, 2022) Bokhari, Ahmed; Baleanu, Dumitru; Belgacem, Rachid; Kumar, Sunil; Baleanu, Dumitru; Djilali, Salih; 56389
In the present work, we study the motion of the projectile using the regularized Prabhakar derivative of order beta. The correlation of physical quantities with units of measurement creates an obstacle in solving some fractional differential equations, as the solutions presented mathematically may not have a physical meaning. To overcome this problem and maintain dimensions of physical quantities, an auxiliary parameter sigma is usually used. We obtain analytical solutions of the velocity fractional differential system in terms of the three parameters Mittag-Leffler function denoted Ea ,beta(z). We recover the cases when applying Caputo and ordinary derivatives. (c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Regularized Prabhakar derivative for partial differential equations
(Univ Tabriz, 2022) Bokhari, Ahmed; Baleanu, Dumitru; Baleanu, Dumitru; Belgacem, Rachid; 56389
Prabhakar fractional operator was applied recently for studying the dynamics of complex systems from several branches of sciences and engineering. In this manuscript, we discuss the regularized Prabhakar derivative ap-plied to fractional partial differential equations using the Sumudu homotopy analysis method(PSHAM). Three illustrative examples are investigated to confirm our main results.
Shehu Transform and Applications to Caputo-Fractional Differential Equations
(Etamaths Publ, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Bokhari, Ahmed; 56389
In this manuscript we establish the expressions of the Shehu transform for fractional Riemann-Liouville and Caputo operators. With the help of this new integral transform we solve higher order fractional differential equations in the Caputo sense. Three illustrative examples are discussed to show our approach.