Document Details

Document Type : Thesis 
Document Title :
LIOUVILLE - CAPUTO TYPE FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL DISCRETE AND INTEGRAL BOUNDARY CONDITIONS
المعادلات التفاضليه الكسريه من نوع ليوفيل - كابوتو مع شروط حدية تكامليه منفصله غير محليه
 
Subject : Faculty of Sciences 
Document Language : Arabic 
Abstract : This thesis studies some new boundary value problems of Liouville-Caputo fractional differential equations, inclusions and coupled systems of fractional differential equations supplemented with several kinds of nonlocal boundary conditions. As a first problem, we discuss the existence and uniqueness of solutions for Liouville-Caputo fractional differential equations of arbitrary order equipped with nonlocal discrete and integral boundary conditions. We also study the Riemann-Stieltjes boundary condition case. This work has been presented in Chapter 2. In Chapter 3, we extend our study initiated in Chapter 2 to the case when the nonlinearity in the fractional differential equation depends on the unknown function together with its lower-order derivative, and flux type strip conditions. Chapter 4 is concerned with the existence of solutions for Liouville-Caputo fractional differential inclusions involving convex and non-convex multivalued maps, supplemented with nonlocal integro-multipoint boundary conditions. In Chapter 5, we investigate a boundary value problem of coupled Liouville-Caputo fractional differential equations with nonlinearities depending on the unknown functions as well as their lower order derivatives, and coupled nonlocal strip and multipoint (discrete) boundary conditions. In the last Chapter, we discuss the solvability of a coupled system of Liouville-Caputo nonlinear fractional differential equations together with nonlocal coupled flux and multipoint strip boundary conditions. The contents of Chapters 2,3,5 and 6 have been published, while the results of Chapter 4 are `under-review'. The detail of the work accomplished in this thesis can be found in the list of publications on the page ix. The background material from analysis and fractional calculus needed for our work is outlined in Chapter 1. 
Supervisor : Dr. Ahmed Eid AlSaadi 
Thesis Type : Doctorate Thesis 
Publishing Year : 1438 AH
2017 AD 
Co-Supervisor : Dr. Bashir Ahmed Mohammed 
Added Date : Monday, June 5, 2017 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
دعاء عبدالرؤف قاروتKarout, Duaa Abdel RaoufResearcherDoctorate 

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