ABSTRACT
This chapter presents the application of Chebyshev wavelets for the solution of fractional order differential equations. It considers fractional order partial differential equations comprising the Caputo fractional derivative and the Riesz fractional derivative. The chapter examines the application of Chebyshev wavelets for the numerical solution of fractional differential equations involving Caputo and Riesz fractional derivatives. It focuses on the two-dimensional Chebyshev wavelet technique for solving nonlinear fractional differential equations like the time-fractional Sawada-Kotera (SK) equation, Riesz fractional Camassa–Holm (CH) equation, and Riesz fractional sine-Gordon equation (SGE) in order to demonstrate the efficiency and accuracy of the proposed method. The classical SK equation is an important mathematical model arising in different physical contexts to describe the motion of long waves in shallow water under gravity and in a one-dimensional nonlinear lattice and has wide applications in quantum mechanics and nonlinear optics. Analyzing the numerical results, the two-dimensional Chebyshev wavelet method provides accurate numerical solutions for fractional differential equations.
