The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal contro...

In this article, we investigate the solution of fractional multidimensional Navier–Stokes equation based on Caputo derivative operator. The behavior regarding system using Sumudu transform approach is discussed analytically and further graphically.

The anomalous (i.e., non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of "random kicks" is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a new fractional equation of the Kramers-Fokker-Planck type is derived. The associated collision operator necessarily involves a fractional substantial derivati...

In the present paper we give a fractional generalization of the Lauwerier formulation of the boundary value problem of the temperature field in oil strata. The Caputo fractional derivative operator and the Laplace transform are the important tools for solving the proposed problem. By using Efros’ theorem which is a modified form of convolution theorem for Laplace transform, the solution is obta...

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...

In a rectangular domain, boundary-value problem is considered for mixed-type equation with regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's fractional derivative. Using method separation variables, Laplace transform, unique solvability has been established. Moreover, we have found explicit solution initial problems derivative non-zero startin...

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 work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...