Solving Some Families of Fractional Order Partial  Differential Equations by Using Laplace Transform Homotopy Perturbation methods

Awoke Wolledie

dc.contributor.author	Awoke Wolledie
dc.date.accessioned	2023-01-12T08:11:09Z
dc.date.available	2023-01-12T08:11:09Z
dc.date.issued	2022-12
dc.identifier.uri	http://ir.bdu.edu.et/handle/123456789/14892
dc.description.abstract	In this project we solve solving some families of fractional order partial differential equations using Laplace transform Homotopy Perturbation methods. The aim of the methods is to find series analytic approximate solution by considering small parameter of differential equations. The method is used to find solutions of both fractional ordinary and fractional partial differential equations. Perturbation methods are based on an assumption that a small parameter must exist in the equation. Determination of small parameter required special art of techniques. An appropriate choice of small parameters leads to ideal results. However, unsuitable choice of small parameter results in bad effects Using ideas of ordinary calculus, we can differentiate a function f (x)  x to the first or second order. We can also establish a meaning or some potential applications of the results. However, can we differentiate the same function, to say, the halves order? Can we establish a meaning or some potential applications of the results? We may not achieve that through ordinary calculus. But we can achieve through fractional calculus, which is a more generalized form of calculus. It is not mean calculus of fractions, rather is the name for the theory of derivatives and integrals of arbitrary order. Fractional derivatives have proven their capability to describe several phenomena associated with memory effects [2]. Their non-locality property is common in physical processes and cosmological problems. They are described by fractional derivatives. Thus fractional calculus is needed. Fractional partial differential equations (FPDEs) have been developed in many different fields of science. They are used to simulating natural physical process and dynamic systems [9]. Solutions of most fractional differential equations are usually nonlinear partial differential equations of science and engineering.	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	Solving Some Families of Fractional Order Partial Differential Equations by Using Laplace Transform Homotopy Perturbation methods	en_US
dc.type	Thesis	en_US