Please use this identifier to cite or link to this item: `http://prr.hec.gov.pk/jspui/handle/123456789/10861`
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dc.contributor.authorhaq, Fazal-
dc.date.accessioned2019-10-04T11:03:13Z-
dc.date.available2019-10-04T11:03:13Z-
dc.date.issued2018-
dc.identifier.govdoc18290-
dc.identifier.urihttp://prr.hec.gov.pk/jspui/handle/123456789/10861-
dc.description.abstractIn last few decades, it has been proved that fractional order differential equations and their systems are very important in mathematical modeling various phenomena of biological, chemical and physical sciences. In addition to these, a fractional calculus also contains many applications in various ﬁelds of engineering and technology. For this propose , differential equations of fractional order is the point of attention in last few years. This project is related with the study of existence theory and numerical solutions of fractional order differential equations. For this study, we ﬁrst review some useful deﬁnitions, notations and results from fractional calculus. Also for the study of numerical solutions, we use a power full techniques. We start our thesis with the study of existence and uniqueness of positive solutions for simple boundary value problem. Then, we obtain necessary and sufﬁcient conditions for existence of at least three positive solutions for the considered models. To solve coupled systems of nonlinear fractional differential equations, we discussamethodwhichisknownasLaplaceAdomiandecompositionmethod(LADM). LADM is an excellent mathematical tool for solving linear and nonlinear differential equations. This method is a combination of the famous integral transform known as Laplace transform and the Adomain decomposition method. In this method, we handle some class of coupled systems of nonlinear fractional order differential equations. Using the proposed method to obtain successfully an exact or approximate solution in the form of convergence series. Thus, we can easily applyLADMto solveawideclassof nonlinearfractionalorderdifferentialequations.The suggested method is applied without any linearization, discretization and unrealistic assumptions. It has been proved that LADM is vary efﬁcient and suitable to solve non-linear problem of physical nature. Some examples are presented to justify the accuracy and performance of the proposed method.en_US
dc.language.isoen_USen_US
dc.publisherHazara University, Mansehraen_US
dc.subjectPhysical Sciencesen_US
dc.subjectMathematicsen_US
dc.titleExistence Theory and Numerical Solutions of The Fractional Order Mathematical Modelsen_US
dc.typeThesisen_US
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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