Existence Of Solutions Of Boundary Value Problems For Several Classes Of Fractional Differential Equations With P-Laplacian Operator

Fractional differential equations is a discipline developed along with the fractionalcalculus. Along with the further development of research, people found that it can de-scribe the phenomena of nature better. Therefore, fractional differential equations playsan important role in many fields such as physics, electrical circuits, biology, control the-ory, etc. Thus, many domestic and foreign scholars have paid more attention to fractionaldifferential equations, especially the existence of solutions.The thesis is divided into five chapters as follows. Chapter one briefly introducessome background and research development of boundary value problems for fractionaldifferential equations, as well as some major work of the thesis. Chapter two and threeconsider the existence of multi-point boundary value problems for Riemanne-Liouville andCaputo fractional differential equations at resonance with p-Laplacian operator under twodimensional kernel space. By using the extension of Mawhin’s continuation theorem, theexistence of solutions are obtained. Chapter four discusses a class of two-point boundaryvalue problems of Caputo fractional delay differential equations with p-Laplacian operator.By using the Guo-Krasnoselskii fixed point theorem, the existence of positive solutions areobtained. Chapter five is the conclusion part.When p=2, the problem can be transformed into the linear operator problem, theconclusion of this paper is also established. Furthermore, based on some known results, weextend kernel space to high-dimensional space and investigate more complicated system.Compared with the previous results, the content of this article either in form or in contentperfect and improve the related research results. Secondly, there are few articles whichconsider boundary value problems of Caputo fractional delay differential equation withp-Laplacian. To a certain extent, our paper generalizes and enriches the related researchresults.