The fractional diffusion equation is one of the important recent models that can efficiently characterize various complex processes, such as in inhomogeneous or heterogeneous media porous media. This article provides a method for numerical simulation time-fractional equations. proposed scheme combines local meshless based on radial basis function (RBF) with Laplace transform. first implements t...

In this paper we investigate existence of solutions for the system: Dtαu=div(u∇p),Dtαp=−(−Δ)sp+u2,in T3 0<s≤1, and 0<α≤1. The term Dtαu denotes Caputo derivative, which models memory effects in time. fractional Laplacian (−Δ)s represents Lévy diffusion. We prove global nonnegative weak that satisfy a variational inequality. proof uses several approximations steps, including an implicit Euler ti...

The spin-4/3 fractional superstring is characterized by a chiral algebra involving a spin-4/3 current on the world-sheet in addition to the energy-momentum tensor. These currents generate physical state conditions on the fractional superstring Fock space. Scattering amplitudes of these physical states are described which satisfy both spurious state decoupling and cyclic symmetry (duality). Exam...

Let Bi be an (Ni, d)-fractional Brownian motion with Hurst index αi (i = 1,2), and let B1 and B2 be independent. We prove that, if N1 α1 + N2 α2 > d , then the intersection local times of B1 and B2 exist, and have a continuous version. We also establish Hölder conditions for the intersection local times and determine the Hausdorff and packing dimensions of the sets of intersection times and int...

Fractional partial differential equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we propose a local discontinuous Galerkin (LDG) method for the distributedorder time and Riesz space fractional convection-diffusion and Schrödinger type equations. We prove stability and optimal order of convergence O(h + (∆t) θ 2 + θ) for the distr...

In the present era, fractional calculus plays an important role in various fields. Fractional Calculus is a field of mathematic study that grows out of the traditional definitions of the calculus integral and derivative operators in much the same way fractional exponents is an outgrowth of exponents with integer value. Based on the wide applications in engineering and sciences such as physics, ...

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...