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This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. On account of the most general character of the derived results, numerous results on fractional reaction, fractional diffusion, and fractional reaction-diffusion problems scattered in the literature, including the recently derived results by the authors for reaction-diffusion models, follow as special cases.
We consider an integral transform introduced by Prabhakar, involving generalised multi-parameter Mittag-Leffler functions, which can be used to introduce and investigate several different models of fractional calculus. We derive a new series expressi
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized fra
The main objective of this article is to present $ u$-fractional derivative $mu$-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new $ u$-fractional derivative satisfies various pro
In this paper, we present an extension of Mittag-Leffler function by using the extension of beta functions ({O}zergin et al. in J. Comput. Appl. Math. 235 (2011), 4601-4610) and obtain some integral representation of this newly defined function. Also
We introduce and study the properties of a new family of fractional differential and integral operators which are based directly on an iteration process and therefore satisfy a semigroup property. We also solve some ODEs in this new model and discuss applications of our results.