Application of the Laplace Transform to a New Form of Fractional Kinetic Equation Involving the Composition of the Galúe Struve Function and the Mittag–Leffler Function

The great importance of the fractional kinetic equations (FKEs) can be seen in the very recent research work of proposing such new equations and finding their solutions by different analytical and numerical methods. The paramount purpose of the present work is to proffer and study new FKEs involving the composition of the generalized Galúe Struve function of first kind and k-Mittag–Leffler function and apply a very influential effective analytical approach based on Laplace transform to find their analytical solutions. The obtained solutions have been presented with some real values and the simulation done via MATLAB. Furthermore, the numerical and graphical interpretations are also mentioned to illustrate the main results. Some special cases are to be taken under consideration to get the results in simpler form.