fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

Riesz potentials also called Riesz fractional derivatives and their Hilbert transforms are computed for the Korteweg-de Vries soliton. They are expressed in terms of the full-range Hurwitz Zeta functions ζ s, a and ζ− s, a . It is proved that these Riesz potentials and their Hilbert transforms are linearly independent solutions of a Sturm-Liouville problem. Various new properties are establishe...

In this paper we introduce the fractional dark energy model, in which accelerated expansion of Universe is driven by a nonrelativistic gas (composed either fermions or bosons) with noncanonical kinetic term. The inversely proportional to cube absolute value momentum for fluid an equation state parameter equal minus one, and whose corresponding density mimics one cosmological constant. general c...

In this work, we consider the nonlocal obstacle problem with a given $\psi$ in bounded Lipschitz domain $\Omega$ $\mathbb{R}^{d}$, such that $\mathbb{K}\_\psi^s={v\in H^s\_0(\Omega):v\geq\psi \text{ a.e. }\Omega}\neq\emptyset$, by $$ u\in\mathbb{K}\_\psi^s:\quad\langle\mathcal{L}au,v-u\rangle\geq\langle F,v-u\rangle\quad\forall v\in\mathbb{K}^s\psi, for $F$ $H^{-s}(\Omega)$, dual space of fract...

n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...