In this article, the researcher considered some well-known mathematical models of ordinary differential equations applied in biology such as bacterial growth, natural FC solution for vegetables, biological phospholipids pathway, glucose absorption by body and spread epidemics. The each model are fractionalized means Caputo derivative a function with respect to certain exponential function. mode...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering...

In this paper, we use the Mittag-Leffler addition formula to solve Green function of generalized time fractional diffusion equation in whole plane and prove convergence function.

In the paper, the authors generalize the notion “k-Mittag-Leffler function”, establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function. 1. Preliminaries Throughout this paper, let C, R, R0 , R, Z − 0 , and N denote respectively the sets of com...

We study generation and propagation properties of Mittag-Leffler moments for solutions of the spatially homogeneous Boltzmann equation for scattering collision kernels corresponding to hard potentials without angular Grad’s cutoff assumption, i.e. the angular part of the scattering kernel is nonintegrable with prescribed singularity rate. These kind of moments are infinite sums of renormalized ...