‎In recent years‎, ‎many methods have been studied for solving differential equations of fractional order‎, ‎such as Lie group method, ‎invariant subspace method and numerical methods‎, ‎cite{6,5,7,8}‎. Among this‎, ‎the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order‎. In this paper we apply this method f...

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...

The main aim of this article is to study an extension the Beta and Gamma matrix functions by using a two-parameter Mittag-Leffler function. In particular, we investigate certain properties these extended such as symmetric relation, integral representations, summation relations, generating relation functional relation.

We aim to introduce extended generalized Mittag-Leffler function (EGMLF) via the Beta and obtain certain integral differential representation of them. Further, we present some formulas Riemann-–Liouville fractional integration differentiation operators. Also, derive various transforms, including Euler transform, Laplace Whittakar transform K-transform. The operator images are expressed in terms...

In this paper, Sumudu transformation (ST) of Caputo fractional derivative formulae are derived for linear differential systems. This formula is applied with Mittage-Leffler function certain homogenous and nonhomogenous systems nonzero initial conditions. Stability discussed by means the system's distinctive equation.

This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for including, Mellin transform, differential formulas, integral representations, essential summation relations. Furthermore, crucial statistical app...