【摘要】：本文共分為二章.第一章主要研究Banach空間中帶有Riemann-Stieltjes型積分條件的非線性分數階積分微分方程的解的存在性和唯一性.通過Green函數的性質、Holder不等式、Banach壓縮映射原理、Schauder不動點定理得到了解的存在性和唯一性結果.第二章主要研究一類帶有Riemann-Stieltjes型積分邊值條件的非線性分數階微分方程解的存在性問題,本文通過利用相關Green函數的不等式以及錐拉伸壓縮不動點定理得到正解的存在性.我們推廣和改進了包括奇異及非奇異兩種情況的一些已知結果.
[Abstract]:This paper is divided into two chapters. In chapter 1, we study the existence and uniqueness of solutions for nonlinear fractional integrodifferential equations with Riemann-Stieltjes type integral conditions in Banach spaces. The existence and uniqueness of the solution are obtained by the properties of Green function, Holder inequality, Banach contraction mapping principle and Schauder fixed point theorem. In the second chapter, we study the existence of solutions for a class of nonlinear fractional differential equations with Riemann-Stieltjes type integral boundary value conditions. In this paper, we obtain the existence of positive solutions by using the inequality of Green function and the fixed point theorem of cone stretching contraction. We generalize and improve some known results including singular and nonsingular cases.
【學位授予單位】：曲阜師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175.6

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1 Dimplekumar;N. CHALISHAJAR;K. KARTHIKEYAN;;EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES[J];Acta Mathematica Scientia;2013年03期

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本文編號：2320411