Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

Abstract

Abstract:In this paper, we investigate the existence of positive solutions for Hadamard type fractional differential system with coupled nonlocal fractional integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii's and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples.

On a System of Hadamard Fractional Differential Equations With Nonlocal Boundary Conditions on an Unbounded Domain

“…The system (1) is supplemented with general nonlocal boundary conditions (2), where the unknown functions Φ and Ψ in the point 1 and their derivatives until orders n − 2 and m − 2, respectively, are all 0, and the Hadamard derivatives of Φ and Ψ of order n − 1 and m − 1 at ∞ are dependent on both Riemann-Liouville integrals of Φ and Ψ. Our problem generalizes the problem studied in [1], by considering here different orders for the fractional derivatives in the equations of system (1), and also a general form of the boundary conditions from (2) at ∞. Under some assumptions on the data of this problem, we gave firstly the solution of the associated linear boundary value problem, and the corresponding Green functions with their properties.…”

“…A positive solution of (1),( 2) is represented by a pair of functions (Φ(υ), Ψ(υ)), υ ∈ [1, ∞) satisfying ( 1) and ( 2 . This problem generalizes the problem from [1]. In the paper [1], the authors studied the system (1) with α, β ∈ (1, 2] (n = m = 2), with the boundary conditions…”

“…This problem generalizes the problem from [1]. In the paper [1], the authors studied the system (1) with α, β ∈ (1, 2] (n = m = 2), with the boundary conditions…”

“…, n. Therefore, in our paper, we consider general orders for the fractional derivatives in the equations of system (1). Furthermore, in the boundary conditions (2), the fractional derivatives H D α−1 1+ Φ and H D β−1 1+ Ψ for ∞ are dependent on both functions Φ and Ψ, in comparison with the condition (3) from [1], where the derivative of Φ is dependent only on Ψ, and the derivative of Ψ is dependent only on Φ. In addition, the conditions (2) with Riemann-Stieltjes integrals generalize, as we saw before, the conditions (3).…”

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

“…Due to the importance of the subject and the possibility of employing it in various scientifc felds, many researchers in the feld of fractional diferential have studied the systems of fractional diferentials equations with a variety of serious conditions accompanying them. For more information about, these scientifc papers, the reader can see [24][25][26][27][28][29][30][31], and the stability of solutions was studied after the existence of them. To enrich the reader, it is possible to see [32][33][34].…”