New Aspects of Bloch Model Associated with Fractal Fractional Derivatives

Abstract

To model complex real world problems, the novel concept of non-local fractal-fractional differential and integral operators with two orders (fractional order and fractal dimension) have been used as mathematical tools in contrast to classical derivatives and integrals. In this paper, we consider Bloch equations with fractal-fractional derivatives. We find the general solutions for components of magnetization ℳ = (Mu, Mv, Mw) by using descritization and Lagrange's two step polynomial interpolation. We analyze the model with three different kernels namely power function, exponential decay function and Mittag-Leffler type function. We provide graphical behaviour of magnetization components ℳ = (Mu, Mv, Mw) on different orders. The examination of Bloch equations with fractal-fractional derivatives show new aspects of Bloch equations.