Green's function for singular fractional differential equations and applications

2022/03/20 by Lee, Jinsil, Lee, Yong-Hoon
#34B15 #34B18 #34B27 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2203.10671

Abstract

In this paper, we study the existence of positive solutions for nonlinear fractional differential equations with a singular weight. We derive Green's function and corresponding integral operator and then examine the compactness of the operator. As an application, we prove an existence-result for positive solutions when a nonlinear term satisfies either superlinear or sublinear conditions. The proof was mainly employed by Krasnoselski's classical fixed point theorem.

Related

• Regularity of solutions for singular fractional differential equation
• Existence, Uniqueness of Positive Solution to a Fractional Laplacians with Singular Nonlinearity
• Sufficient Conditions for Existence of Positive Solutions for a Caputo Fractional Singular Boundary Value Problem
• Existence of a unique positive solution for a singular fractional boundary value problem
• Positive Green's functions for some fractional-order boundary value\n problems