Shahrezaee,M.Arabameri,M.Ahmadian,A.2024-05-252024-05-25202402211-379710.1016/j.rinp.2024.1076062-s2.0-85190553441https://doi.org/10.1016/j.rinp.2024.107606https://hdl.handle.net/20.500.14517/1739Bloch 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. © 2024eninfo:eu-repo/semantics/closedAccessFractional Bloch equationsGeneralized Laplace transformψ-Caputo derivativeArticleQ1Q160