The Approximate Solution for Multi-term the Fractional Order Initial Value Problem Using Collocation Method Based on Shifted Chebyshev Polynomials of the First Kind

Abstract

Nowadays, to survive and promote the market competition, multi-item business strategy is more effective for any production/manufacturing sector. Many physical problems can be best model by using fractional differential equation (FDE). In this paper, we propose the approximate scheme to solve multi-term fractional order initial value problem. The proposed scheme is based on collocation method and shifted Chebyshev polynomials (SCP). The fractional derivatives are utilized in the Caputo sense. The fractional order initial value problem can be reduced to a system of algebraic equations by utilizing the properties of SCP, which is solved numerically. The collocation point is chosen in such a way as to attain stability and convergence. The main theme of the proposal is to centralize the upper bound of the derived formula and convergence analysis. The numerical examples are achieved good accuracy using proposed scheme even by using small number of shifted Chebyshev polynomials.