Abstract In this paper, we concentrate on the Lie symmetry structure of a system multi-dimensional time-fractional partial differential equations (PDEs). Specifically, first give an explicit prolongation formula involving Riemann–Liouville derivative for infinitesimal generator in case, and then show that has elegant structure. Furthermore, present two simple conditions to determine generators ...

It is well known that methods for solving fractional-order PDEs are grossly inadequate compared with integer-order PDEs. In this paper, a new approach combined the separation method of semi-fixed variables and dynamical system introduced. As an example, time-fractional reaction-diffusion equation higher-order terms studied under two different kinds differential operators. parametric regions, ph...

In the present research paper, an iterative approach named Shehu transform method is implemented to solve time-fractional hyperbolic telegraph equations in one, two, and three dimensions, respectively. These are prominent ones field of physics some other significant problems. The efficacy authenticity proposed tested using a comparison approximated exact results graphical form. Both 2D 3D plots...

Abstract This paper introduces sufficient conditions to determine conservation laws of diffusion equations arbitrary fractional order in time. Numerical methods that satisfy discrete counterparts these have approximate the continuous ones. On basis this result, we derive for a mixed scheme combines finite difference method space with spectral integrator A range numerical experiments shows conve...

In this paper, we introduce the non-conformable double Laplace transform. Its properties are studied, and it is applied to solve some fractional PDEs involving nonconformable derivative. Graphical representations of obtained solutions shown in figures. The study shows that transform effective easy apply create an exact solution for types PDEs.

In this paper we introduce a stochastic integral with respect to the solution X of the fractional heat equation on [0, 1], interpreted as a divergence operator. This allows to use the techniques of the Malliavin calculus in order to establish an Itô-type formula for the process X.

The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long WaveBurgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker’s parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational for...

In this work, we proposed a hybrid algorithm to approximate the solution of Conformable Fractional Fokker-Planck Equation (CFFPE). This comprises unification two methods named Wave Transformation Method (FWTM) and Differential Transform (DTM). The method is based on steps. first step reduce given CFPDEs corresponding Partial Equations (PDEs). Then, second solve obtained PDEs iteratively by usin...

Abstract Obtaining the numerical approximation of fractional partial differential equations (PDEs) is a cumbersome task. Therefore, more researchers regarding approximated-analytical solutions such complex-natured PDEs (FPDEs) are required. In this article, analytical-approximated fractional-order coupled Burgers’ equation provided in one-, two-, and three-dimensions. The proposed technique nam...

This research work is dedicated to solving the n-generalized Korteweg–de Vries (KdV) equation in a fractional sense. The method combination of Sumudu transform and Adomian decomposition method. has significant advantages for differential equations that are both linear nonlinear. It easy find solutions fractional-order PDEs with less computing labor.