Positive solutions of $p$-Laplacian fractional differential equations with fractional derivative boundary condition

Fractional Laplacian, homogeneous Sobolev spaces and their realizations

We study the fractional Laplacian and the homogeneous Sobolev spaces on R^d , by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit correspondence between these two spaces, and show that they admit the same representation. Along the way we also prove some properties of the fractional Laplacian.

Infinitely Many Weak Solutions for Fractional Dirichlet Problem with $p$-Laplacian

We focus on the study of $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the genus properties in critical point theory, we establish some new criteria to guarantee the existence of infinitely many weak solutions for the considered problem.

Ground State Solutions of Kirchhoff-type Fractional Dirichlet Problem with $p$-Laplacian

We consider the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the Nehari method in critical point theory, we obtain the existence theorem of ground state solutions for such Dirichlet problem.

p-Laplacian Fractional Sturm-Liouville Problem for Diffusion Operator via Impulsive Condition

In this study, the existence results of solution is given for fractional p-Laplacian Stum-Liouville problem for diffusion operator of order with impulsive conditions. The derivatives are described in Riemann-Liouville and Caputo sense. The Riemann-Liouville integral operator is used to acquire the integral representation of solution. The existence of solution is demonstrate via Schaefer fixed point theorem.

Existence and Multiplicity of Nontrivial Weak Solutions for Kirchhoff-type Fractional $p$-Laplacian Equation

We discuss the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the mountain pass theorem and the genus properties in critical point theory, we get some new results on the existence and multiplicity of nontrivial weak solutions for such Dirichlet problem.

分数阶拉普拉斯的梅林定义

Mellin definition of the fractional Laplacian

本文基于梅林变换为分数阶拉普拉斯提出新等价定义，适用于径向函数，并修正了Riesz分数阶导数的文献公式，且验证于空间分数阶扩散方程。