Scale-3 Haar wavelet-based method of fractal-fractional differential equations with power law kernel and exponential decay kernel

Abstract

In this study, wavelet method has been proposed to solve fractal-fractional differential equations (FFDEs) with power law kernel (FFDPL) and exponential decay kernel (FFDED). The proposed method is based on scale 3 Haar wavelets with collocation method, and fractional integral operational matrices for derivatives of Caputo and Caputo–Fabrizio sense are derived to solve FFDPL and FFDED. The applicability of the proposed method is shown by solving some numerical examples, and the obtained results are compared with available solutions in the literature. The solutions are presented in the graphical and tabular forms also.

Keywords

• fractal-fractional differential equations
• haar wavelet
• singular and nonsingular kernels
• collocation method