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 this paper, a collocation method based on the Bernstein polynomials is presented for the fractional Riccati type differential equations. By writing t? ta (0 < a < 1) in the truncated Bernstein series, the truncated fractional Bernstein series is obtained and then it is transformed into the matrix form. By using Caputo fractional derivative, the matrix forms of the fractional derivatives are ...

In this work, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation using conformable derivative. The Riccati method is used to get analytical solutions space-fractional equation. Because has never been examined with and multiplicative noise at same time, generalize some previous results. Moreover, display how influences on stability of obtained

Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei–Norman method is applied for obtaining the associated differential equation in the group SL(2,R). The superposition principle for first order differential equation systems and Lie-Scheffers theorem are also analysed f...

This study investigates the new (3+1)-dimensional shallow water wave equation. To do so, definitions of conformable derivatives and their descriptions are given. Using Riccati equation modified Kudryashov methods, exact solutions to this problem discovered. The gathered data's contour plot surfaces related 3D 2D emphasize result's physical nature. monitor problem's activity, complete necessary....

The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by fractional-order differential equation. First, as an example of such system, viscoelastically damped structure is selected. Second, LQR designed for in which terms are contained the equation motion. An iteration-based method solving algebraic Riccati proposed order obtain feedback gains LQR. ...

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.