The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order di...

The time fractional heat conduction in an infinite plate of finite thickness, when both faces are subjected to boundary conditions of second kind, has been studied. The time fractional heat conduction equation is used, when attempting to describe transport process with long memory, where the rate of heat conduction is inconsistent with the classical Brownian motion. The stability and convergenc...

We consider a harmonic chain perturbed by an energy conserving noise depending on a parameter γ . When γ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when γ = 0, the energy superdiffuses according to a 3/4 fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existenc...

This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the suc...

Fractional integro-differential equations arise in the mathematical modelling of various physical phenomena like heat conduction in materials with memory, diffusion processes etc. In this paper, we have taken the fractional integro-differential equation of type Dy(t) = a(t)y(t) + f(t) + ∫ t

A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["N...

In this effort, we propose a new fractional differential operator in the open unit disk. The is an extension of Atangana-Baleanu without singular kernel. We suggest it for normalized class analytic functions By employing extended operator, study time-2-D space heat equation and optimizing its solution by chaotic function.