In this paper, we use a method based on the operational matrices to the solution of the fractional partial differential equations. The main approach is based on the operational matrices of the Haar wavelets to obtain the algebraic equations. The fractional derivatives are described in Caputo sense. Some examples are included to demonstrate the validity and applicability of the techniques.
In this paper, variational homotopy perturbation iteration method (VHPIM) has been applied along with Caputo derivative to solve high-order fractional Volterra integro-differential equations (FVIDEs). The “VHPIM” is present in all two steps. In order to indicate the efficiency and simplicity of the proposed method, we have presented some examples. All of the numerical computations in this study have been done on a personal computer applying some programs written in Maple18.
We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.
Abstract. In this paper, we are going to investigate the canonical property of solutions of systems of differential equations having a singularity and turning point of even order. First, by a replacement, we transform the system to the Sturm-Liouville equation with turning point. Using of the asymptotic estimates provided by Eberhard, Freiling, and Schneider for a special fundamental system of solutions of the Sturm-Liouville equation, we study the infinite product representation of solutions of the systems. Then we transform the Sturm-Liouville equation with turning point to the equation with singularity, then we study the asymptotic behavior of its solutions. Such representations are relevant to the inverse spectral problem.
This paper deals with a newly born fractional derivative and integral on time scales. A chain rule is derived, and the given indefinite integral is being discussed. Also, an application to the traffic flow problem with a fractional Burger's equation is presented.
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