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

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 cal...

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主要作者: Ahmood, Wasan Ajeel
格式: Thesis
語言:English
出版: 2017
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spelling my-upm-ir.709082019-08-07T04:43:24Z Extension of laplace transform to multi-dimensional fractional integro-differential equations 2017-05 Ahmood, Wasan Ajeel 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. Laplace transformation 2017-05 Thesis http://psasir.upm.edu.my/id/eprint/70908/ http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf text en public doctoral Universiti Putra Malaysia Laplace transformation
institution Universiti Putra Malaysia
collection PSAS Institutional Repository
language English
topic Laplace transformation


spellingShingle Laplace transformation


Ahmood, Wasan Ajeel
Extension of laplace transform to multi-dimensional fractional integro-differential equations
description 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.
format Thesis
qualification_level Doctorate
author Ahmood, Wasan Ajeel
author_facet Ahmood, Wasan Ajeel
author_sort Ahmood, Wasan Ajeel
title Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_short Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_full Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_fullStr Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_full_unstemmed Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_sort extension of laplace transform to multi-dimensional fractional integro-differential equations
granting_institution Universiti Putra Malaysia
publishDate 2017
url http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf
_version_ 1747812933937659904