Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations

Abstract

Abstract In the present paper, an efficient method based on a new kind of Chebyshev wavelet together with Picard technique is developed for solving fractional nonlinear differential equations with initial and boundary conditions. The new orthonormal Chebyshev wavelet basis is constructed from a class of orthogonal polynomials called the fifth-kind Chebyshev polynomials. The convergence analysis and error estimation of the proposed Chebyshev wavelet expansion are studied. An exact formula for the Riemann-Liouville fractional integral of the Chebyshev wavelet is derived. Picard iteration is used to convert the fractional nonlinear differential equations into a fractional recurrence relation and then the proposed Chebyshev wavelet collocation method is applied on the converted problem. Several test problems are given to illustrate the performance and effectiveness of the proposed method and compared with the existing work in the literature.