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...

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 ...

BACKGROUND Data derived from studies of fishers' local ecological knowledge (LEK) can be invaluable to the proposal of new studies and more appropriate management strategies. This study analyzed the fisher's LEK about trophic relationships of fishes in the southeastern Brazilian coast, comparing fishers' LEK with scientific knowledge to provide new hypotheses. METHODS The initial contacts wit...

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...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

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...

In this paper, the projective Riccati equation method is applied to find exact solutions for fractional partial differential equations in the sense of modified RiemannLiouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the vali...

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...