Applications of Fractional Order Mathematical Models with an Effective Integral Transform

Abstract

The Sumudu transform is a type of mathematical integral transform similar to the Laplace and Fourier transforms. It is used to solve differential equations and control engineering problems. By extending the traditional notion of derivatives to non-integer orders, fractional derivatives bring the concept of differentiation to fractional orders. This concept is associated with fractional calculus, a mathematical field that deals with arbitrary, non-integer order differentiation and integration. This study takes into account the logistic equation, the blood alcohol model with unique fractional derivatives, and Newton’s law of cooling in a number of modeling problems. The Sumudu transform is used to get the analytical answers, and figures are used to model the results in various orders. The derivative proposed by Caputo Fabrizio and Atangana Baleanu is extended to fractional derivatives with Mittag-Leffler and exponential-decay kernels. We also investigated the effects of the power-law kernel by Caputo and constant proportional Caputo derivatives. To demonstrate how the answers are simulated, we offer a few figures. We have shown the efficiency of the Sumudu transform on several models.