Numerical algorithm to solve generalized fractional pantograph equations with variable coefficients based on shifted Chebyshev polynomials

Abstract

ABSTRACTIn this paper, an efficient numerical technique based on the shifted Chebyshev polynomials (SCPs) is established to obtain numerical solutions of generalized fractional pantograph equations with variable coefficients. These polynomials are orthogonal and have compact support on . We use these polynomials to approximate unknown solutions. Using the properties of the SCPs, we derive the generalized pantograph operational matrix of SCPs and the one of fractional-order differentiation. Then, based on these matrices the original problem is transformed into a system of algebraic equations. By solving these algebraic equations, we can obtain numerical solutions. In addition, we investigate the error analysis and introduce the process of error correction for improving the precision of numerical solutions. Lastly, by giving some examples and comparing with other existing methods, the validity and efficiency of our method are demonstrated.