Existence of a positive solution to a class of fractional differential equations

Positive solutions for a semipositone fractional boundary value problem with a forcing term

“…Then, applying these properties and the well known Krasnosel'skii fixed point theorem in cones, he derived sufficient conditions for the existence of at least one positive solution of the problem. The existence of positive solutions is not studied in [9] when the nonlinear term g is a sign-changing function.…”

“…The monographs [14,19] and the papers [13,16,18,20] are excellent sources for the theory and applications of fractional calculus. Among all the topics, the existence of positive solutions of BVPs of fractional differential equations has been extensively studied by many researchers in recent years; see, for example, [1,2,3,6,7,8,9,11,21,23] and the references therein. In particular, Goodrich [9] studied the BVP consisting of the equation [9], the author first obtained some properties of the Green's function associated with the problem.…”

“…Among all the topics, the existence of positive solutions of BVPs of fractional differential equations has been extensively studied by many researchers in recent years; see, for example, [1,2,3,6,7,8,9,11,21,23] and the references therein. In particular, Goodrich [9] studied the BVP consisting of the equation [9], the author first obtained some properties of the Green's function associated with the problem. Then, applying these properties and the well known Krasnosel'skii fixed point theorem in cones, he derived sufficient conditions for the existence of at least one positive solution of the problem.…”

Positive solutions for a class of fractional differential coupled system with integral boundary value conditions

“…In consequence, many meaningful results in these fields have been obtained. See [1,2,3,4,5,12,13,15] for a good overview.…”

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

“…It has wide range of applications in various fields of science and engineering such as physics, mechanics, control systems, flow in porous media, electromagnetics and viscoelasticity. For some of the recent developments in fractional calculus, we refer to Miller and Ross [19], Samko, Kilbas and Marichev [22], Podlubny [20], Kilbas, Srivasthava and Trujillo [15], Kilbas and Trujillo [16], Diethelm [4], Diethelm and Ford [5], Lakshmikantham and Vatsala [18], Goodrich [7] and the references therein.…”