In this article, by using the monotone iterative technique coupled with the method of upper and lower solution, we obtain the existence of extremal iteration solutions to conformable fractional differential equations involving Riemann-Stieltjes integral boundary conditions. At the same time, the comparison principle of solving such problems is investigated. Finally, an example is given to illustrate our main results. It should be noted that the conformal fractional derivative is essentially a modified version of the first-order derivative. Our results show that such known results can be translated and stated in the setting of the so-called conformal fractional derivative.

In this paper, we discuss a nonlinear fractional order boundary value problem with nonlocal Erdélyi-Kober and generalized Riemann-Liouville type integral boundary conditions. By using Mawhin continuation theorem, we investigate the existence of solutions of this boundary value problem at resonance. It is shown that the boundary value problemhas at least one solution under some suitable conditions, where α, β ∈ R, 0 < ζ , ξ < T.

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 Dαx(t)=f(t,x),  t∈[0,1], x(0)=∫01x(t)dA(t), where Dαx(t) is the standard conformable fractional derivative of order α, 0<α≤1, and f∈C([0,1]×R,R). Simultaneously, the fixed point theorem for set-valued increasing operator is applied when considering the given problem.

This paper deals with the following Caputo fractional differential equations with Riemann-Stieltjes integral boundary conditions ( ) ( ) denotes the Riemann-Stieltjes integrals of with respect to . By mean of coincidence degree theory, we obtain the existence of solutions for the above fractional BVP at resonance. In the end, according to the main results, we give a typical example.

This paper is concerned with the existence of extremal solutions for periodic boundary value problems for conformable fractional differential equations with deviating arguments. We first build two comparison principles for the corresponding linear equation with deviating arguments. With the help of new comparison principles, some sufficient conditions for the existence of extremal solutions are established by combining the method of lower and upper solutions and the monotone iterative technique. As an application, an example is presented to enrich the main results of this article.