Generalized sine-cosine wavelet method for Caputo-Hadamard fractional differential equations

In this article, a wavelet method is introduced for solving Caputo-Hadamard fractional differential equations on an arbitrary interval. The proposed method is the fractional-order generalization of sine-cosine wavelets (FGSCWs). The operational matrices of fractional-order integration are constructed for solving initial value problem as well as boundary value problem. Furthermore, numerical solution of nonlinear Caputo-Hadamard fractional differential equation is obtained with the conjunction of proposed method with quasilinearization technique. We have constructed the FGSCW operational matrix, FGSCW operational matrix of Hadamard fractional integration of arbitrary order, and FGSCW operational matrix of Hadamard fractional integration for Caputo-Hadamard fractional boundary value problems. Convergence analysis of the proposed method is investigated. Numerical procedure is given for both Caputo-Hadamard initial and boundary value problems. Illustrative examples show the reliability and efficiency of the proposed method and give solution with less error.