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Approximate analytical solution for nonlinear system of fractional differential equations by BPS operational matrices. (English) Zbl 1273.34004
Summary: We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and, in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI). The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches one.
MSC:
34A08Fractional differential equations
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34A45Theoretical approximation of solutions of ODE