Multiplicity results to a conformable fractional differential equations involving integral boundary condition (Q2325203)

Summary: In this article, by using topological degree theory couple with the method of lower and upper solutions, we study the existence of at least three solutions to Riemann-Stieltjes integral initial value problem of the type \(D_\alpha x(t) = f(t, x), t \in [0,1]\), \(x(0) = \int_0^1 x(t) d A(t)\), where \(D_\alpha x(t)\) is the standard conformable fractional derivative of order \(\alpha\), \(0 < \alpha \leq 1\), and \(f \in C([0,1] \times \mathbb{R}, \mathbb{R})\). Simultaneously, the fixed point theorem for set-valued increasing operator is applied when considering the given problem.