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Extension of laplace transform to multi-dimensional fractional integro-differential equations


Ahmood, Wasan Ajeel (2017) Extension of laplace transform to multi-dimensional fractional integro-differential equations. PhD thesis, Universiti Putra Malaysia.

Abstract / Synopsis

The main focus of this thesis is to extend the study of one-dimensional fractional to multi-dimensional fractional calculus and study of multi-dimensional Laplace transformation with their respective applications. This extension will be used to solve special types of multi-dimensional fractional calculus such as space-time partial fractional derivative. The multi-dimensional Laplace transforms method used to solve the multi-dimensional fractional calculus with constant and variable coefficients and the multidimensional modification of Hes variational iteration method to solve the multi-dimensional fractional integro-differential equations with non-local boundary conditions are developed. The study of multi-dimensional space-time fractional derivative with their applications and also, new fractional derivative and integral including Riemann-Liouville having a non-local and non-singular kernel are detailed. Finally, we obtained the exact solution of multi-dimensional fractional calculus, space-time partial fractional derivative and the system of matrix fractional differential equation in Riemann- Liouville sense of matrices but there are some problems that cannot be solved analytically, thus we solved them by multi-dimensional variational iteration method. This study shows that integral transform can be used to present new solutions to problems by certain applications for solving them.

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Additional Metadata

Item Type: Thesis (PhD)
Subject: Laplace transformation
Call Number: FS 2017 42
Chairman Supervisor: Professor Adem Kılıcman, PhD
Divisions: Faculty of Science
Depositing User: Editor
Date Deposited: 07 Aug 2019 12:43
Last Modified: 07 Aug 2019 12:43
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