Study of solutions of fractional order differential equations

Abstract

Here in project, we centralize on the presence and singularity of gentle arrangements, and their approximations of a class of development conditions of vital and fractional orders involving deviating arguments and impulses. Evolution equations are usually dealt with the governing partial differential equations of many physical phenomena in Hilbert spaces or more generally, in Banach spaces and may be viewed as ordinary differential equations in an infinite dimensional state space. Although, the term has no accurate definition, and its significance depends on the actual situation, yet in addition on the detailing of the issue for which it is utilized. Many physical phenomena like reaction diffusion equations, laser optics, coupled oscillators, enzyme kinetics, food webs, control theory, climate models, viscosity materials, population ecology, the heat conduction and the wave propagation in materials are naturally modeled by abstract functional differential equations in Hilbert spaces (or in Banach spaces), where the space variables are merged with the domain of the operator.