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.
In literature, there are many methods for solving nonlinear partial differential equations. In this paper, we develop a new method by combining Adomian decomposition method and Shehu transform method for solving nonlinear partial differential equations. This method can be named as Shehu transform decomposition method (STDM). Some examples are solved to show that the STDM is easy to apply.
In this paper, we are interested on the Shehu transform of both Prabhakar and HilferPrabhakar fractional derivative and its regularized version. These results are presented in terms of Mittag-Leer type function and also utilized to obtain the solutions of some Cauchy type problems, such as Space-time Fractional Advection-Dispersion equation and Generalized fractional Free Electron Laser (FEL) equation, at which Hilfer-Prabhakar fractional derivative of fractional order and its regularized version are involved.
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.
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