Document Details

Document Type : Thesis 
Document Title :
A study of differential equations involving different fractional derivatives
دراسة المعادلات التفاضلية التي تتضمن مشتقات كسرية مختلفة
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : This thesis is concerned with the study of some boundary value problems involving Caputo, Hilfer, ψ-Hilfer fractional derivative operators equipped with different kinds of boundary conditions. In the first problem, we investigate a boundary value problem for fractional differential equations involving ψ-Hilfer fractional derivative, supplemented with nonlocal multi-point boundary conditions. The second problem deals with the existence of solutions for a boundary value problem of Hilfer type coupled sequential fractional differential equations equipped with integro-multistrip-multipoint boundary conditions. In the third problem, we continue the study of the second (single-valued) problem discussed in chapter three to its multivalued variant. In the fourth problem, we investigate a coupled system of Caputo type nonlinear fractional differential equations with boundary conditions in terms of sum and difference of the governing functions. The last problem studies the existence theory for a coupled system of nonlinear Liouville–Caputo fractional differential equations complemented with nonlocal boundary conditions. The methods of modern analysis are applied to develop the existence theory for the proposed problems. The results achieved for the first and fourth problems have been respectively published in “Dynamic Systems and Applications” and “AIMS Mathematics” journal, while the results obtained for the second and third problems have been accepted for publication in the journal: “Fixed Point Theory”. The work accomplished for the fifth problem will appear in the journal: “Miskolc Mathematical Notes”. For details, see the list of publications on page x. The mathematical background related to our study is outlined in Chapter 1. The results established for the five problems studied in this thesis are respectively presented in Chapters 2, 3, 4, 5 and 6. 
Supervisor : Prof. Ahmed Alsaedi 
Thesis Type : Doctorate Thesis 
Publishing Year : 1444 AH
2023 AD 
Co-Supervisor : Prof. Bashir Ahmad 
Added Date : Thursday, June 29, 2023 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
فوزية محمد العتيبيAlotaibi, Fawziah MohammedResearcherDoctorate 

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