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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:

34A08 Fractional ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A45 Theoretical approximation of solutions to ordinary differential equations
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