In this paper, a new construction of exact solutions based on the improved generalized Riccati equation mapping method with modified Reimann-Luiviile fractional derivative and symbolic computation is proposed for seeking abundant solutions of the space-time fractional fifth-order nonlinear Sawada-Kotera equation. The proposed method is very simple, direct, effective and convenient for obtaining...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

Keywords: Fractional differential equations Impulsive fractional differential equations Impulse General solution Existence a b s t r a c t In this paper, for impulsive differential equations with fractional-order q 2 ð0; 1Þ, we show that the formula of solutions in cited papers are incorrect. Secondly, we find out a formula of the general solution for impulsive Cauchy problem with Caputo fracti...

In this paper we construct new random walks connected with fractional order differential equations. Namely, the governing equations corresponding to the constructed random walks are multi-term or distributed fractional order differential equations. Nowadays the connection between random walk and fractional order dynamics is well known, see, for instance [1, 17, 26, 33, 38]. A number of construc...

Recently, fractional differential equations are applied widely in various fields of science and engineering. Regarding applications of fractional differential equations, we refer to 1– 15 and references cited therein. However, the investigation of basic theory of fractional differential equations is still not complete, and there is a great deal of work which needs to be done. Most of the invest...

Nuclear magnetic resonance (NMR) is a physical phenomenon widely used to study complex materials. NMR is governed by the Bloch equation, a first order non-linear differential equation. Fractional order generalization of the Bloch equation provides an opportunity to extend its use to describe a wider range of experimental situations. Here we present a fractional generalization of the Bloch equat...

where α ∈ (, ], f : [, ]×R→R (R := (–∞, +∞)) is continuous. In view of a fractional differential equation’s modeling capabilities in engineering, science, economy and other fields, the last few decades have resulted in a rapid development of the theory of fractional differential equation; see the books [–]. This may explain the reason why the last few decades have witnessed an overgrowing...

*Correspondence: [email protected] Department of Science, Huaihai Institute of Technology, Cangwu Road, Lianyungang, 222005, China Abstract We apply the Chebyshev polynomial-based differential quadrature method to the solution of a fractional-order Riccati differential equation. The fractional derivative is described in the Caputo sense. We derive and utilize explicit expressions of weighting coef...

Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is des...