Document Details

Document Type : Thesis 
Document Title :
Fractional-order boundary value problems involving generalized derivatives and integrals
مسائل القيم الحدية الكسرية غير الخطية التي تشمل المشتقات والتكاملات المعممة
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : In this thesis, we have studied some new nonlocal initial-boundary value problems of generalized and Caputo-type generalized fractional differential equations, inclusions and coupled systems supplemented with different kinds of boundary conditions. Chapter 1 contains preliminary concepts of fractional calculus and fixed point theory. In Chapter 2, we obtain the sufficient conditions for the uniqueness of solutions for a boundary value problem of fractional differential equations involving generalized fractional derivative, and Stieltjes and generalized fractional integral boundary conditions. Chapter 3 deals with the existence of solutions for generalized fractional differential equations and inclusions complemented with generalized fractional integral boundary conditions. We make use of the standard fixed point theorems for single-valued and multivalued maps to obtain the desired results. In Chapter 4, we study a new fractional-order integro-initial value problem involving a Caputo-type generalized fractional derivative and Steiltjes type fractional integral. Extremal solutions for the given problem are obtained by applying monotone iterative technique. Sufficient conditions ensuring the existence of solutions for the given problem are also obtained. Then we switch onto the study of Caputo-type generalized fractional differential inclusions with Steiltjes-type fractional initial conditions. In the first part of Chapter 5, we investigate the existence and uniqueness of solutions for nonlinear impulsive multi-order Caputo-type generalized fractional differential equations supplemented with nonlocal integro-initial value conditions involving generalized fractional integrals. Extremal solutions for the given problem are also presented. The second part of Chapter 5 deals with a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. Chapter 6 is concerned with the study of a nonlinear Langevin fractional differential equation involving Caputo-type generalized fractional differential operators of different orders and equipped with nonlocal generalized integral boundary conditions. The multivalued case of this problem for convex and non-convex valued maps is also discussed. In the last Chapter, we introduce and investigate a new coupled system of mixed Caputo and Riemann-Liouville generalized fractional differential equations subject to coupled integral boundary conditions. The contents of Chapter 2, 3, 4, 5 and 6 have been published in SCI Journals, while the results presented in Chapter 7 are "Under Review". 
Supervisor : Prof. Dr. Ahmed Alsaedi 
Thesis Type : Doctorate Thesis 
Publishing Year : 1441 AH
2020 AD 
Co-Supervisor : Prof. Dr. Bashir Ahmad 
Added Date : Saturday, May 30, 2020 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
مديحه مبروك الغانميAlghanmi, Madeaha MabroukResearcherDoctorate 

Files

File NameTypeDescription
 46255.pdf pdf 

Back To Researches Page