Using shifted Legendre scaling functions for solving fractional biochemical reaction problem. (English) Zbl 1499.92027
Summary: In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matrix of fractional integration and collocation technique, the main problem is transformed to a set of non-linear algebraic equations. This obtained algebraic system can be solved by available standard iterative procedures. Numerical results of applying the proposed method are investigated in details.
MSC:
| 92C40 | Biochemistry, molecular biology |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34A08 | Fractional ordinary differential equations |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
Keywords:
Legendre scaling functions; fractional biochemical reaction problem; Caputo derivative; collocation methodReferences:
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