Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices | Zendy

Mohsen Alipour | Zendy; Dumitru Băleanu | Zendy

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Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices

Author(s) -

Mohsen Alipour,

Dumitru Băleanu

Publication year - 2013

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2013/954015

Subject(s) - fractional calculus , mathematics , nonlinear system , derivative (finance) , matrix (chemical analysis) , order (exchange) , mathematical analysis , differential equation , physics , materials science , finance , quantum mechanics , financial economics , economics , composite material

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 1

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