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 fractional calculus. With the further development of research, some people find that it can describe the phenomena nature better. Therefore,fractional differential equations plays an important role in many fileds such as physics,electrical circuits,biology,controltheory,etc.Thus,many domestic and foreign scholars have paid more attention to fractional differential equations,especially the existence of solutions.The article mainly utilizes the extension of Mawhin’s continuation theorem and fixed point theorem as well as some inequation techniques to conduct a more in-depth study on the existence of solutions of multi-point boundary value problems for several classes of fractional differential equations with p-Laplacian operator and the multi-point boundary value problems on a half-line,which achieved the some existence theorem of solution.The thesis is divided into five chapters as follows.Chapters one briefly introduces some background and research development of boundary value problems for fractional differential equations, as well as some major work of the thesis.Chapter two utilizes the extension of Mawhin’s continuation theorem to discuss the exitence of solutions for fractions multi-point boundary value problems with p-Laplacian operator at resonance.Chapter three discussed the exitence of solutions for fractions multi-point boundary value problems with p-Laplacian operator at resonance on a Half-line. Chapter four in the light of fixed-point theorems,some sufficient conditions are obtained to quarantee the existence of at least one solution of the boundary value problems at nonresonance.Chapter five is the concllusion part.To a certain extent, our paper generalize and enrich the related research results.