The objective of this article is to present the computable solution of space-time advection-dispersion equation of fractional order associated with Hilfer-Prabhakar fractional derivative operator as well as fractional Laplace operator. The method followed in deriving the solution is that of joint Sumudu and Fourier transforms. The solution is derived in compact and graceful forms in terms of the generalized Mittag-Leffler function, which is suitable for numerical computation. Some illustration and special cases of main theorem are also discussed.
In this paper, we have studied the concentration profile of Cytosolic calcium ion (Ca[Formula: see text] with the aid of fractional calculus. A mathematical model has been considered to examine the influence of fractional advection diffusion equation (cross flow) for the calcium profile. A closed form solution of the fractional advection diffusion equation, arising in study of diffusion of cytosolic calcium in astocytes cell, has been obtained by using Sumudu transform techniques. Graphs for the calcium concentration profiles have been simulated for certain values of the parameters to examine the various effects on concentrations of Cytosolic calcium ion.
This article is devoted to study Elzaki transform and its applications in Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative. We derive formula of Elzaki transform for Hilfer-Prabhakar derivative and its regularized version. The solution of Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative of fractional order is presented in terms of Mittag-Leffler type function. Furthermore, we find the application of the generalized Hilfer-Prabhakar derivative in linear partial differential equation and some problems of Mathematical Physics.
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