Department Colloquium

Location: CL 435

Speaker: Mathew Aibinu, University of Regina

Title:  Solutions of fractional differential models by using Sumudu transform method and its hybrid

Abstract:

Fractional calculus extends differentiation to non-integer orders and provides an amazing platform for the description of various kinds of systems. Moreover, time delay in differential equations plays amazing roles by making the differential equations to be more precise as models for real-life systems. Delay differential equations are the essential platform for the consideration of the hereditary properties of the physical systems. In recent decades, there have been exceptional advancement efforts on the construction of approximate analytical and numerical solutions of differential equations. Solutions of differential equations have been considered by using several analytical and numerical methods. Most of these approaches are not hitch free due to their association with certain impediments that include divergent results, un-realistic assumptions, calculation of Adomian's polynomials, very lengthy calculations, limited convergence and non-compatibility with the nonlinearity of physical problems. This study presents an integral transform method and its hybrid for the construction of solutions of differential equations. The study presents two suitable methods with brief computation steps that produce exact solutions of differential equations of integer and non-integer orders. The study considers the mathematical model for the decay of Iodine 135 as an application of fractional differential equations in nuclear physics. The application indicates that fractional differential equations with variable delay proportional to the independent variable are a useful tool for the modelling of many anomalous phenomena in nature and in the theory of complex systems.