In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theorems such as Banach contraction mapping principle, Krasnoselskii's fixed point theorem, and Leray-Schauder nonlinear alternative. Further, we present Ulam-Hyers stability results by using direct analysis methods. Different types of Ulam stability, such as Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability, are studied. Examples which support our theoretical results are also presented.

Based on the properties of nonlocal fractional calculus generated by conformable derivatives, we establish some sufficient conditions for oscillation of all solutions for fractional differential equations with damping term. Forced oscillation of conformable differential equations in the frame of Riemann, as well as of Caputo type, is established. Examples are provided to demonstrate the effectiveness of the main results.

In this paper, we investigate the existence and uniqueness of symmetric solutions for fractional differential equations with multi-order fractional integral boundary conditions, by means of standard fixed point theorems. Examples which support our theoretical results are also presented. MSC: 34A08; 34B15

<abstract><p>In this paper, we investigate the existence result for $ (k, \psi) $-Riemann-Liouville fractional differential equations via nonlocal conditions on unbounded domain. The main result is proved by applying a fixed-point theorem for Meir-Keeler condensing operators with a measure of noncompactness. Finally, two numerical examples are also demonstrated to confirm the usefulness and applicability of our theoretical results.</p></abstract>