Existence Of Solutions For Some Boundary Value Problems Of Fractional P-Laplacian Equations By Using The Upper And Lower Solutions Method

As is well known, fractional differential equation theory is a branch of the the-ory of differential equation. It has a broad real application background in physics, chemistry, biology and control theory. With the rapid development of science and tech-nology, the research of fractional differential equation, especially for boundary value problem, has become to be recognized as an important research field.By using the upper and lower solutions method and the fixed point theory, we study the existence of solutions of boundary value problems of fractional differential equations. The thesis contains the following sections:Section 1 introduces the historical background and some recent results of the frac-tional differential equation obtained in the literature and our main work in this thesis; few people made use of the Nagumo condition to discuss the existence of solutions for fractional differential equation;Section 2 mainly makes use of the Nagumo condition to study the existence of solutions of boundary value problems for the fractional differential equations with p-Laplacian operator, and obtain the existence conditions, which improves the existing results;Section 3 discusses the existence of solutions of boundary value problems for frac-tional differential equations with p-laplacian operator. The requirement for the nonlin-earity f is weaker than the Nagumo condition which is commonly used;Section 4 discusses the existence and uniqueness of solution to boundary value problem for fractional differential equations, and our proof depends on fixed point the-orem;Fanally, section 5 gives a summary and prospect of this paper.This paper totally includes 58 references.