Shifted Chebyshev Polynomials with Residual Power Series Method for Solving Various Types of Models

Recently, Chebyshev’s polynomials have attracted much attention in finding solutions for fractional order differential equations (FODEs). In this research study, we represent shifted second-kind Chebyshev orthonormal polynomials (SSKCOP) with residual power series (RPS) technique to solve various types of models such as diffusion model, Backward Kolmogorov model, homogeneous and nonhomogeneous advection models taking into account with time fractional derivative in Caputo manner. By utilization of SSKCOP and their orthogonality properties, these models will be reduce into system of FODEs which can be solved by using RPS technique. The numerical simulations and outcomes are presented through various graphs and tables demonstrating that present method is accurate and powerful to obtain approximate solutions of non-linear models that arise in engineering and physics.