Document Details

Document Type : Thesis 
Document Title :
Fractional Differential Equations with Nonlocal Boundary Conditions
معادلات تفاضلية كسرية مع شروط حدية غير محلية
 
Subject : mathematics department 
Document Language : Arabic 
Abstract : In this thesis, some boundary value problems of fractional differential equations and inclusions are studied. As a first problem, we have investigated a four-point nonlocal boundary value problem of nonlinear fractional integro-differential equations of order q∈(1,2] in Chapter 2. The existence of solutions to the given problem is shown by applying Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. The uniqueness of solutions to the problem is established by using Banach's contraction mapping principle. Our results are new and several special cases can be obtained by fixing the parameters involved in the problem. The contents of this chapter have appeared in the article: “A nonlocal integral boundary value problem of nonlinear integro-differential equations of fractional order, International Journal of the Physical Sciences, 2012; 7(42), 5648-5653”. As a second problem, we consider nonlinear fractional differential inclusions with nonlocal four-point integral boundary conditions in Chapter 3 and obtain some new existence results. Our tools of study include the nonlinear alternative of Leray Schauder type together with the selection theorem of Bressan and Colombo for lower semi-continuous maps with decomposable values and Wegrzyk's fixed point theorem for multivalued maps. These results have been published in the paper: “Existence results for fractional differential inclusions involving non-convex valued maps with four-point nonlocal integral boundary conditions, Communications in Mathematical Analysis, 14 (2013), No. 1, pp. 15-27”. 
Supervisor : Prof. Bashir Ahmad 
Thesis Type : Master Thesis 
Publishing Year : 1434 AH
2013 AD 
Added Date : Monday, June 24, 2013 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
صفاء عبدالمعــطي السلميAl-Solamy, Safa’a AbdulmotiResearcherMaster 

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