In this work, the fractional Lie symmetry method is used to find exact solutions of time-fractional coupled Drinfeld-Sokolov-Wilson equations with Riemann-Liouville derivative. Time-fractional are obtained by replacing first-order time derivative derivatives (FD) order $\alpha$ in classical (DSW) model. Using method, generators obtained. With help generators, FCDSW reduced into ordinary differe...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-know...

In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these is a locally uniformly convergent power series that can be chosen adequately to obtain family fractional and, in particular, main existing derivatives. Based on conditions for Laplace transform operators, some new results are obtained—for example, relationships between Rie...

in this paper, inverse laplace transform method is applied to analytical solution of the fractional sturm-liouville problems. the method introduces a powerful tool for solving the eigenvalues of the fractional sturm-liouville problems. the results  how that the simplicity and efficiency of this method.

In this paper we prove new Opial-type inequalities for arbitrary kernels using superquadratic functions, also their extensions are obtained. Furthermore, find fractional versions by applying different kinds of integral and derivative operators.

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of the fractional mater...

We study mixed Riemann-Liouville fractional integration operators and derivative in Marchaud form of function two variables Hölder spaces different orders each variables. The obtained are results generalized to the case with power weight.