Fractal-fractional differential and integral equations are well-defined at t = 0

Overview & Synopsis

Differential and integral equations with fractal-fractional operators are important classes of equations used to model processes with complex behaviors. For example, a fractal-fractional derivative with power law can be viewed as a product of the Riemann-Liouville derivative and the power law function. In the last year, a question was raised to know what happens when the initial point is 0, especially when dealing with a numerical scheme. In this paper, we aim to solve those problems for all different fractal-fractional differential and integral operators and present some illustrative examples.