Numerical solution of fractional Sturm-Liouville equation in integral form

Abstract

In this paper a fractional differential equation of the Euler-Lagrange / Sturm-Liouville type is considered. The fractional equation with derivatives of order $\alpha \in \left(0,1\right]$ in the finite time interval is transformed to the integral form. Next the numerical scheme is presented. In the final part of this paper examples of numerical solutions of this equation are shown. The convergence of the proposed method on the basis of numerical results is also discussed.

14 pages, 3 figures, 2 tables

References in corpus (3)

• Green's Theorem for Generalized Fractional Derivatives
• Towards a combined fractional mechanics and quantization
• The DuBois-Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler-Lagrange Equation Involving only Derivatives of Caputo

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• Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order
• Sharp asymptotics in a fractional Sturm-Liouville problem
• Fractional Sturm-Liouville eigenvalue problems, II