Generalized Fibonacci operational collocation approach for fractional initial value problems. (English) Zbl 1411.11015
Summary: A numerical algorithm for solving multi-term fractional differential equations (FDEs) is established herein. We established and validated an operational matrix of fractional derivatives of the generalized Fibonacci polynomials (GFPs). The proposed numerical algorithm is mainly built on applying the collocation method to reduce the FDEs with its initial conditions into a system of algebraic equations in the unknown expansion coefficients. Output of the numerical results asserted that our developed algorithm is applicable, efficient and accurate.
MSC:
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 34A08 | Fractional ordinary differential equations |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
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