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 matrices of ...

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. 

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of differential equation of integer order connected with inverse forms of Abel-integral equations. The algorithm is used for solution of the linear and non-linear equati...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

In this paper, Crank-Nicholson method for solving fractional wave equation is considered. The stability and consistency of the method are discussed by means of Greschgorin theorem and using the stability matrix analysis. Numerical solutions of some wave fractional partial differential equation models are presented. The results obtained are compared to exact solutions.

In this paper, a spectral Tau method for solving fractional Riccati differential equations is considered. This technique describes converting of a given fractional Riccati differential equation to a system of nonlinear algebraic equations by using some simple matrices. We use fractional derivatives in the Caputo form. Convergence analysis of the proposed method is given and rate of convergence ...

In this paper, by using the coincidence degree theory, we consider the following two-point boundary value problem for fractional differential equation { D 0+x(t) = f(t, x(t), x ′(t)), t ∈ [0, 1], x(0) = 0, x′(0) = x′(1), where D 0+ denotes the Caputo fractional differential operator of order α, 1 < α ≤ 2. A new result on the existence of solutions for above fractional boundary value problem is ...

In this paper, Sumudu decomposition method is developed to solve general form of fractional partial differential equation. The proposed method is based on the application of Sumudu transform to nonlinear fractional partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivatives are described in the Caputo sense. The Sumud...

In this article we study a new class of boundary value problems for fractional differential equations and inclusions with multiple orders of fractional derivatives and integrals, in both fractional differential equation and boundary conditions. The Sadovski’s fixed point theorem is applied in the single-valued case while, in multi-valued case, the nonlinear alternative for contractive maps is u...