Generalized Fibonacci Operational Collocation Approach for Fractional Initial Value Problems

  • A. G. Atta
  • G. M. Moatimid
  • Y. H. Youssri
Original Paper


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.


Fractional differential equations Generalized Fibonacci sequence Spectral methods 

Mathematics Subject Classification

11B39 65N35 34A08 34A12 



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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationAin Shams University, RoxyCairoEgypt
  2. 2.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt

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