Abstract: In this paper, we are implemented the Chebyshev spectral method for solving the non-linear fractional Klein-Gordon equation (FKGE). The fractional derivative is considered in the Caputo sense. We presented an approximate formula of the fractional derivative. The properties of the Chebyshev polynomials are used to reduce FKGE to the solution of system of ordinary differential equations...

This paper is concerned with the initial value problem to a nonlinear fractional difference equation with the Caputo like difference operator. By means of some fixed point theorems, global and local existence results of solutions are obtained. An example is also provided to illustrate our main result.

In the paper unconstrained local controllability problem of finite-dimensional fractional discrete-time semilinear systems with constant coefficients is addressed. Using general formula of solution of difference state equation sufficient condition for local unconstrained controllability in a given number of steps is formulated and proved. Simple illustrative example is also presented.

In this paper, an efficient numerical method is considered for solving the fractional wave equation (FWE). The fractional derivative is described in the Caputo sense. The method is based on Laguerre approximations. The properties of Laguerre polynomials are utilized to reduce FWE to a system of ordinary differential equations, which is solved by the finite difference method. An approximate form...

We present a finite difference/spectral method for the two-dimensional generalized time fractional cable equation by combining second-order backward difference in and Galerkin spectral space with Legendre polynomials. Through detailed analysis, we demonstrate that scheme is unconditionally stable. The proved to have min{2−α,2−β}-order convergence accuracy smooth solutions, where α,β are two exp...

In this paper, the numerical method for a multiterm time-fractional reaction–diffusion equation with classical Robin boundary conditions is considered. The full discrete scheme constructed L1-finite difference method, which entails using L1 on graded meshes temporal discretisation of each Caputo fractional derivative and finite uniform spatial discretisation. By dealing carefully, sharp error a...

Abstract This paper will solve one of the fractional mathematical physics models, a one-dimensional time-fractional differential equation, by utilizing second-order quarter-sweep finite-difference scheme and preconditioned accelerated over-relaxation method. The proposed numerical method offers an efficient solution to equation applying computational complexity reduction approach technique. app...