Eigenvalues for iterative systems of Sturm-Liouville fractional order two-point boundary value problems

Abstract

In this paper, we determine the eigenvalue intervals of λ 1 , λ 2 , · · ·, λ n for which the iterative system of nonlinear Sturm-Liouville fractional order two-point boundary value problem possesses a positive solution by an application of Guo-Krasnosel'skii fixed point theorem on a cone.MSC 2010 : Primary 26A33; Secondary 34B15, 34B18

Eigenvalues for iterative systems of Riemann–Liouville type p-Laplacian fractional-order boundary-value problems in Banach spaces

“…Prasad and Krushna (2013) established the existence of multiplicity of positive solutions to the coupled system of FBVPs by utilizing Legett-Williams fixed point theorem. Later, the authors in Prasad and Krushna (2014b) extend these results to the iterative system of fractional-order differential equations together with two-point boundary conditions. In this article, we consider the iterative system of p-Laplacian fractional-order differential equations:…”

On a coupled system of fractional order differential equations with Riemann-Liouville type boundary conditions

“…The theory of fractional order differential equations is growing rapidly. Recently, much attention has been paid to the study of the existence of positive solutions of fractional order differential equations satisfying initial and boundary conditions; see [1,2,3,4,5,6,7,8] and the references therein. The multi-point boundary value problems for ordinary differential equations appear in a variety of areas of applied mathematics, physics and engineering.…”

Existence of solutions for a coupled system of three-point fractional order boundary value problems

“…Recently, much interest has been created in establishing positive solutions for boundary value problems associated with ordinary and fractional order differential equations. To mention the related papers along these lines, we refer to Erbe and Wang [6], Davis, Henderson, Prasad, and Yin [5] for ordinary differential equations, Henderson and Ntouyas [8,9], Henderson, Ntouyas, and Purnaras [10] for systems of ordinary differential equations, Bai and Lü [3], Kauffman and Mboumi [11], Benchohra, Henderson, Ntoyuas, and Ouahab [4], Khan, Rehman, and Henderson [12], Prasad and Krushna [16,17], Prasad, Krushna, and Sreedhar [18] for fractional order differential equations.…”