This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

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...

In this paper, a new fractional Riccati equation rational expansion method is proposed to establish new exact solutions for fractional differential equations. For illustrating the validity of this method, we apply it to the nonlinear fractional Sharma-TassoOlever (STO) equation, the nonlinear time fractional biological population model and the nonlinear fractional foam drainage equation. Compar...

In this paper operational matrix of Bernstein Polynomials (BPs) is used to solve Bratu equation. This nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. Elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. By using operational matrix of fractional integration...

Recently, one debate in the literature is whether the fractional Schródinger equation in an infinite potential well has the same eigenfunctions as those of its standard (non-fractional) counterpart. Due to the nonlocality of the fractional Laplacian, it is challenging to find the eigenvalues and eigenfunctions of the fractional Schródinger equation analytically. In this talk, we numerically stu...

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...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

In this paper fractional generalization of Liouville equation is considered. We derive fractional analog of normalization condition for distribution function. Fractional generalization of the Liouville equation for dissipative and Hamiltonian systems was derived from the fractional normalization condition. This condition is considered as a normalization condition for systems in fractional phase...