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Abstract In this article, we consider the existence of at least one positive solution to the three-point boundary value problem for nonlinear fractional-order differential equation with an advanced argument where 2 < α ≤ 3, 0 < η < 1, , CDα is the Caputo fractional derivative. Using the well-known Guo-Krasnoselskii fixed point theorem, sufficient conditions for the existence of at least one positive solution are established. MSC (2010): 34A08; 34B18; 34K37.

Values of λ are determined for which there exist positive solutions of the system of dynamic equations, , , for , satisfying the boundary conditions, , where is a time scale. A Guo-Krasnosel'skii fixed point-theorem is applied.

We will establish sufficient conditions for the existence of integral solutions and extremal integral solutions for semilinear functional differential equations with nondensely defined operators in Banach spaces.

The well-known Krasnoselskii twin fixed point theorem is used to investigate the existence of mild solutions for first- and second-order impulsive semilinear functional and neutral functional differential equations in Hilbert spaces.

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson's type inequality for differentiable convex functions using a new parameterized q -integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.

We establish some new noninstantaneous impulsive inequalities using the conformable fractional calculus., Competing Interests: The authors declare that they have no competing interests.

By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractional q-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example.

This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations with Dirichlet boundary conditions. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.

In recent years, a remarkably large number of inequalities involving the fractional q-integral operators have been investigated in the literature by many authors. Here, we aim to present some new fractional integral inequalities involving generalized Erdélyi-Kober fractional q-integral operator due to Gaulué, whose special cases are shown to yield corresponding inequalities associated with Kober type fractional q-integral operators. The cases of synchronous functions as well as of functions bounded by integrable functions are considered.