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Deanship of Graduate Studies
Document Details
Document Type
:
Thesis
Document Title
:
A New Class of Anti-Periodic Fractional Boundary Value Problems
أنواع جديدة من مسائل القيم الحدية الكسرية غير الدورية
Subject
:
mathematics department
Document Language
:
Arabic
Abstract
:
This thesis deals with some boundary value problems of fractional differential equations of order q ϵ (2,3] with anti-periodic fractional boundary conditions. In Chapter 2, we show the existence of solutions for a fully anti-periodic fractional boundary value problem with the nonlinearity dependent upon the unknown function only by means of some fixed point theorems. The problem discussed in this chapter is compared with a fractional boundary value problem having classical anti-periodic boundary conditions and a useful relationship between the solutions of these problems is presented. These results have been published in the Journal: Abstract and Applied Analysis [On a new class of anti-periodic fractional boundary value problems, Abstract and Applied Analysis, 2013 (2013), Article ID 606454]. In the second problem, we allow the nonlinear function in the problem considered in Chapter 2 to depend on the unknown function together with its fractional derivative of order 0<α<1and establish an existence result for this problem by applying Schauder's fixed point theorem in Chapter 3. Finally, in Chapter 4, we discuss the uniqueness of solutions for the problem considered in Chapter 3 and for a more general anti-periodic fractional boundary value problem with the nonlinearity containing the unknown function together with its two lower order fractional derivatives of order α and α+1 by using Banach's contraction mapping principle. Some preliminary facts about fractional calculus are outlined in Chapter 1.
Supervisor
:
prof.Ahmed Alsaedi
Thesis Type
:
Master Thesis
Publishing Year
:
1434 AH
2013 AD
Co-Supervisor
:
prof. Bashir Ahmad
Added Date
:
Wednesday, July 31, 2013
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
ناديه محمد فارع
Farea, Nadya Mohammed
Researcher
Master
Files
File Name
Type
Description
35779.pdf
pdf
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