Systems of semipositone discrete fractional boundary value problems

Abstract

AbstractWe consider the existence of at least one positive solution to the discrete fractional systemwhere , . Due to the fact that and are allowed to be negative for some values of t, , and , we consider here the semipositone problem. In addition to discussing conditions under which this problem is guaranteed to have at least one positive solution for sufficiently small values of , we provide an example to illustrate the use of our results.Keywords:: discrete fractional calculussemipositone problempositive solutionconenonlinear systemKeywords:: Primary: 26A33, 39A10Secondary: 47H07 Notes1. Email: rdahal@coastal.edu2. Email: dduncan@coastal.edu