Journal ArticleDOI
The multistage homotopy analysis method: application to a biochemical reaction model of fractional order
TLDR
Numerical comparisons between the MHAM and the classical fourth-order Runge–Kutta method in the case of integer-order derivatives reveal that the new technique is a promising tool for nonlinear systems of integer and fractional order.Abstract:
In this paper, a new reliable algorithm called the multistage homotopy analysis method (MHAM) based on an adaptation of the standard homotopy analysis method (HAM) is presented to solve a time-fractional enzyme kinetics. This enzyme–substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The new algorithm is only a simple modification of the HAM, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems. Numerical comparisons between the MHAM and the classical fourth-order Runge–Kutta method in the case of integer-order derivatives reveal that the new technique is a promising tool for nonlinear systems of integer and fractional order.read more
Citations
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Proceedings ArticleDOI
Bernstein Polynomials Method to Solve Fractional Model of Basic Enzyme Kinetics
Abstract: Approximate solutions of fractional model of biochemical reaction using Bernstein polynomials method are derived in this paper. Enzyme-substrate reaction system is formed by a system of nonlinear ordinary differential equations. Fractional orders for the system are investigated at α = 0.6, α = 0.75, α = 0.90 and α = 1, to see the behavior of the system when the order is fraction between zero and one, 0 < α ≤ 1.
Journal ArticleDOI
Analytical Solution of Hyperchaotic Zhou Equations by Multistage Homotopy Analysis Method
TL;DR: In this paper, a multistage homotopy analysis approach is used to construct a convergent series in terms of the exponential combination and polynomial functions that use a few terms of this series to obtain higher accuracy.
Journal ArticleDOI
A multiple-step adaptive pseudospectral method for solving multi-order fractional differential equations
TL;DR: In this paper, a multiple-step adaptive pseudospectral method for solving nonlinear multi-order fractional initial value problems (FIVPs), based on piecewise Legendre-Gauss interpolation, is presented.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.