In this paper, based on certain variable transformation, we apply the known (G’/G) method to seek exact solutions for three fractional partial differential equations: the space fractional (2+1)-dimensional breaking soliton equations, the space-time fractional Fokas equation, and the spacetime fractional Kaup-Kupershmidt equation. The fractional derivative is defined in the sense of modified Rie...

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

We compare the Riemann–Liouville fractional integral (fI) of a function f(z) with the Liouville fI of the same function and show that there are cases in which the asymptotic expansion of the former is obtained from those of the latter and the difference of the two fIs. When this happens, this fact occurs also for the fractional derivative (fD). This method is applied to the derivation of the as...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

This paper deals with the existence and uniqueness of solution for a coupled system Hilfer fractional Langevin equation non local integral boundary value conditions. The novelty this work is that it more general than works based on derivative Caputo Riemann-Liouville, because when ? = 0 we find Riemann-Liouville 1 derivative. Initially, give some definitions notions will be used throughout work...

The fractional Laplacian and the fractional derivative are two different mathematical concepts (Samko et al, 1987). Both are defined through a singular convolution integral, but the former is guaranteed to be the positive definition via the Riesz potential as the standard Laplace operator, while the latter via the Riemann-Liouville integral is not. It is noted that the fractional Laplacian can ...

In the present study, our focus is to obtain different analytical solutions space–time fractional Bogoyavlenskii equation in sense of Jumaries-modified Riemann–Liouville derivative and conformable time–fractional-modified nonlinear Schrödinger that describes fluctuation sea waves propagation water ocean engineering, respectively. The G′G2–expansion method applied investigate dynamics solitons r...

Abstract In this paper, we study a system of nonlinear Riemann–Liouville fractional differential equations with delays. First, define in an appropriate way initial conditions which are deeply connected the derivative used. We introduce generalization practical stability call time. Several sufficient for time obtained using Lyapunov functions and modified Razumikhin technique. Two types derivati...