Nonlocal boundary value problems for nonlineartoppled system of fractional differential equations

Abstract

The aim of this paper is to study multiplicity results for the solutions of a coupled system offractional differential equations. The problem under consideration is subjected to nonlocalboundary conditions involving Riemann-Liouville integrals and derivatives of fractionalorder. Necessary and sufficient conditions are established for the existence of at leastone and more solutions by using various fixed point theorems of cone type. Moreoversufficient conditions for uniqueness is also discussed by using a concave type operatorfor the considered problem. Further, the conditions are also provided under which theconsidered system has no positive solution. The results are demonstrated by providingseveral examples.