Abstract
This paper concerns on two types of integral boundary value problems of a nonlinear fractional differential system, i . e ., nonlocal strip integral boundary value problems and coupled integral boundary value problems. With the aid of the monotone iterative method combined with the upper and lower solutions, the existence of extremal system of solutions for the above two types of differential systems is investigated. In addition, a new comparison theorem for fractional differential system is also established, which is crucial for the proof of the main theorem of this paper. At the end, an example explaining how our studies can be used is also given.
Highlights
Differential equations with integral boundary conditions have been applied in many fields such as thermoelasticity, blood flow phenomena, and groundwater systems
By employing the method of upper and lower solutions combined with the monotone iterative technique, we studied a class of nonlinear fractional differential system involving nonlocal strip and coupled integral boundary conditions
We investigated the existence of extremal system of solutions for the above nonlinear fractional differential system involving nonlocal strip and coupled integral boundary conditions
Summary
Differential equations with integral boundary conditions have been applied in many fields such as thermoelasticity, blood flow phenomena, and groundwater systems. By using the Schauder fixed-point theorem, the authors successfully obtained the existence of solution of the system Inspired by these papers, we concern on the following nonlinear Riemann–Liouville fractional differential system of order 0 < α ≤ 1: Dαφ( ε ) F( ε, φ( ε ), ψ( ε ), φ( θ( ε ) ) ),. It is believed that this is an attempt to apply the monotone iterative method to solve nonlinear Riemann–Liouville fractional differential systems with deviating arguments and families of nonlocal coupled and strip integral boundary conditions. To this end, we study the following two types of integral boundary conditions:. If ] ⟶ 0, τ ⟶ L, the condition is degenerated to a classic integral boundary condition (see [42] for details)
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