New orthogonal hybrid function based numerical method to solve system of fractional order differential equations

TL;DR

This paper introduces a new orthogonal hybrid function-based numerical method for efficiently solving systems of fractional order differential equations, demonstrating its accuracy through various biological models.

Contribution

It develops a novel hybrid function approach with operational matrices for fractional integrals, enhancing computational efficiency and accuracy over existing methods.

Findings

Successfully solves fractional models for smoking, lung cancer, and Hepatitis B.

Proves the convergence and reliability of the proposed method.

Demonstrates improved accuracy and efficiency in numerical solutions.

Abstract

In this paper, an easy-to-implement and computationally effective numerical method based on the new orthogonal hybrid functions is developed to solve system of fractional order differential equations numerically. The new orthogonal hybrid functions are hybrid of the piecewise constant orthogonal sample-and-hold functions and the piecewise linear orthogonal right-handed triangular functions. The proposed method uses the generalized one-shot operational matrices which approximate the Riemann-Liouville fractional order integral in the orthogonal hybrid function domain. The convergence of the numerical method is studied. Illustrative examples such as fractional order smoking model, fractional order model for lung cancer, fractional order model of Hepatitis B infection etc. are solved by the proposed numerical method. The results prove the validity and reliability of the proposed numerical method.