Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations

Journal Article · Sun Jul 15 04:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-017-0547-5· OSTI ID:22769256

In this study, we propose a new set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Fractional differential equations are the best tools for modelling natural phenomenon that are elaborated by fractional calculus. Therefore, we need an accurate and efficient technique for solving them. The main purpose of this article is to generalize new functions based on Lagrange polynomials to the fractional calculus. At first, we present a new representation of Lagrange polynomials and in continue, we propose a new set of fractional-order functions which are called fractional-order Lagrange polynomials (FLPs). Besides, a general formulation for operational matrices of fractional integration and derivative of FLPs on arbitrary nodal points are extracted. These matrices are obtained using Laplace transform. The initial value problems is reduced to the system of algebraic equations using the operational matrix of fractional integration and collocation method. Also, we find the upper bound of error vector for the fractional integration operational matrix and we indicate convergence of approximations of FLPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

• OSTI ID: 22769256
• Journal Information: Computational and Applied Mathematics, Journal Name: Computational and Applied Mathematics Journal Issue: 3 Vol. 37; ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CONVERGENCE
DIFFERENTIAL EQUATIONS
LAPLACE TRANSFORMATION
MATRICES
NUMERICAL SOLUTION
POLYNOMIALS
SIMULATION