Abstract
This paper addresses a computational technique for the numerical solutions of nonlinear distributed-order fractional boundary value equations with singular coefficients. The proposed strategy is based on the shifted Legendre-series expansion and the composite midpoint quadrature rule. Moreover, a collocation technique is utilized to reduce the understudy equations to a system of nonlinear algebraic equations solved by Newton’s iteration formula. The \(l_{2}\) and \(l_{\infty }\)-norm errors and experimental convergence order are selected as criteria to analyze the accuracy and precision of the proposed strategy. The results of the performed numerical simulations illustrate the reliability and validity of the proposed approach.
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Communicated by José Tenreiro Machado.
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Arianfar, M., Moghaddam, B.P. & Babaei, A. Computational technique for a class of nonlinear distributed-order fractional boundary value problems with singular coefficients. Comp. Appl. Math. 40, 190 (2021). https://doi.org/10.1007/s40314-021-01576-6
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DOI: https://doi.org/10.1007/s40314-021-01576-6
Keywords
- Numerical approach
- Fractional Calculus
- Distributed order
- Singular coefficients
- Nonlinear partial differential equations
- Shifted Legendre polynomials