Approximate analytical solutions to delay fractional differential equations with Caputo derivatives of fractional variable orders and applications

Fractional derivatives are suitable for describing several physical phenomena. The construction of efficient analytical and numerical methods for the solutions of ordinary and partial fractional differential equations is an active research area and it is of great interest to the researchers. The Caputo fractional derivative is of great use in the modelling and simulation of phenomena where consideration is given to the interactions within the past and problems with nonlocal properties. This study considers the use of a hybrid of the Sumudu Transform method for constructing the solution of nonlinear equations that describe the processes in the functional and structural materials. This study considers the models that are given by the integer-order derivatives, Caputo derivatives of fractional variable orders and Caputo derivatives of fractional variable orders that are associated with delays. The study applies a hybrid of Sumudu Transform to present solutions for each considered model and makes use of graphs to show the correlation among the models. The study is of great importance in the numerical and experimental characterization of the decay properties of functional and structural materials.