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Title: Qualitative Aspects and Numerical Simulations of Coupled Systems of Pantograph Equations via Fractional
Authors: Ahmad, Israr
Keywords: Physical Sciences
Issue Date: 2021
Publisher: University of Malakand, Chakdara
Abstract: In this dissertation, different kinds of nonlinear coupled systems involving proportional type delay fractional order differential equations are considered. The proposed problems are considered under different kinds of fractional derivatives including Caputo, Hadamard and variable order, etc. The aim of the thesis is to develop some theoretical analysis of the proposed problems about existence theory and stability analysis. Sufficient conditions for existence and uniqueness of solutions for nonlinear fractional pantograph differential equations with the help of classical fixed point theory of Krasnoselskii‚Äôs, Leray Schauder type, Banach contraction, etc. are developed. To establish necessary and sufficient con ditions for Hyers-Ulam type stability, tools of nonlinear functional analysis are used. On the other hand numerical analysis is very prominent aspect to be investigated, where exact or analytical solutions for linear and nonlinear problems are impossible. A powerful and useful method known as Haar wavelet collocation is used for pantograph type equations for their numerical analysis. For each aspect, pertinent examples to demonstrate our results are provided. Also in numerical analysis various simulations are provided to justify the method and to conclude the efficiency of adopted techniques.
Gov't Doc #: 23494t
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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