LOWER AND UPPER SOLUTIONS FOR GENERAL TWO-POINT FRACTIONAL ORDER BOUNDARY VALUE PROBLEMS

Abstract

This paper establishes the existence of a positive solution of fractional order two-point boundary value problem, Dq1 a+ y(t) + f(t, y(t)) = 0, t &#8712; [a, b], y(a)=0, y&#8242; (a)=0, &#945;Dq2 a+ y(b) &#8722; &#946;Dq3 a+ y(a)=0, where Dqi a+ , i = 1, 2, 3 are the standard Riemann-Liouville fractional order derivatives, 2 < q1 &#8804; 3, 0 < q2, q3 < q1, &#945;, &#946; are positive real numbers and b>a &#8805; 0, by an application of lower and upper solution method and fixed-point theorems.