Studies on lie group analysis of Certain fractional ordinary Differential equations

Abstract

Generalisation is an important aspect in the development of any newlinetheoretical branch of Mathematics. The generalisation of ordinary integer order newlinederivatives to arbitrary order derivatives is dealt with in fractional calculus. In newlinecontrast to classical derivatives, fractional derivatives are nonlocal in nature. newlineThis property of fractional derivatives aids in the modelling of many natural newlinephenomena that are dependent on past history of time. As a result, the study of newlinefractional differential equations is essential as they are a more appropriate tool newlinein various branches of science and engineering. newlineThe exact solution of any differential equation aids us in newlineunderstanding the physics and geometric aspects of a real-world problem. newlineObtaining the exact solutions to fractional differential equations, on the newlineother hand, is a difficult task. This is because the properties of fractional newlinederivatives are more complicated than the properties of classical derivatives. newlineFurthermore, there is no unified definition for fractional derivative. There newlineare numerous definitions for fractional derivatives in the literature, such newlineas Riemann-Liouville fractional derivative, Caputo fractional derivative, newlineGr¨unwald-Letnikov fractional derivative, Kober fractional derivative, and newlineso on. However, only fractional differential equations (FODEs) with newlineRiemann-Liouville (R-L) fractional derivative are studied in this thesis. newline