We study a full discretization scheme for the stochastic linear heat equationwhen B˙ is very rough space-time fractional noise. The procedure divised into three steps: (i) regularization of noise through mollifying-type approach; (ii) (smoothened) as finite sum Gaussian variables over rectangles in [0,1]×R; (iii) operator on (non-compact) domain [0,1]×R, along principles Galerkin elements metho...

A time-fractional heat equation arising in a quiescent medium is established, and its approximate analytical solution obtained by the fractional power series method. The results show that method performs extremely well terms of efficiency simplicity.

We consider the time-fractional Cattaneo equation involving tempered Caputo space-fractional derivative. There is an increasing interest in recent literature for applications of fractional-type equations to heat transfer models. Our main aim discuss role played by a fractional operator this framework. show that fundamental solution coincides with probability law time-changed Brownian motion, ob...

We consider the linear stochastic wave equation with spatially homogenous Gaussian noise, which is fractional in time with index H > 1/2. We show that the necessary and sufficient condition for the existence of the solution is a relaxation of the condition obtained in [10], when the noise is white in time. Under this condition, we show that the solution is L(Ω)-continuous. Similar results are o...

This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for s...

The purpose of this paper is to study the fuzzy fractional differentialequations. We prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. Fuzzy derivative is considerin the Goetschel-Voxman sense and fractional derivative is consider in theRiemann Liouville sense. At the end, we...

Abstract: Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag–Leffler functio...

In the present article, we use modified homotopy perturbation method (HPM) to find approximate analytical solution of three-dimensional time fractional microscale heat transport equation. This transport equation is at first converted into the equation of two functions. First one have both, the first order fractional time derivative and second order space derivatives, while second one has only s...

Based on the quadratic spline function, a quadratic spline collocation method is presented for the time fractional bioheat equation governing the process of heat transfer in tissues during the thermal therapy. The corresponding linear system is given. The stability and convergence are analyzed. Some numerical examples are given to demonstrate the efficiency of this method. c ©2016 All rights re...