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Title NUMERICAL STUDY AND STABILITY ANALYSIS OF PARABOLIC EQUATION OF FRACTIONAL ORDER

Author(s) Moin Ashraf

Abstract Nowadays the research community prefers fractional calculus over classical calculus, as fractional calculus (FC) has extensively explored the physical properties of fractional-order differentials and integrals. The main reason behind this is that classical calculus deals with more specific behavior, whereas fractional calculus deals with more generic behavior. In this framework, this thesis witnesses the numerical study of the fractional-order parabolic equations. In the modeled problem the fractional-order derivative is assumed in the Caputo sense due to its numerous advantages—the modeled time-fractional parabolic problem is discretized using the Crank-Nicolson method. The thesis also provides a comprehensive study of stability and convergence analysis of the proposed mathematical method. To demonstrate the accuracy as well as efficiency of the scheme, numerical problems with various fractional order derivatives are finally given and compared with the exact solutions. Furthermore, a comparative numerical study is done to demonstrate the efficiency of the proposed method. The thesis is finally summarised in the conclusion.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2024-05-02

Subject Mathematics

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