On the [formula omitted]-Caputo fractional Bloch equations and analytical solutions

Abstract

Bloch equations (BEs) are widely applied in physics, chemistry, magnetic resonance imaging (MRI), and nuclear magnetic resonance (NMR); these equations determine the dynamic equivalence among externally applied magnetic fields and internal model relaxation times. In this article, we generalize the fractional Bloch equations (FBEs) by using a fractional derivative of a function with respect to another function (Ψ-Caputo derivative) and obtain Ψ-Caputo FBEs; then, we use the generalized Laplace transform method (GLTM) for solving the FBEs analytically. We compared the analytical solutions of the Ψ-Caputo FBEs with several functions of Ψ(t) and different values of fractional orders. According to the results, we have shown that the presented method is efficient.