Alexandru Tudorache

We investigate the existence and multiplicity of positive solutions for an ω-Riemann-Liouville fractional differential equation on an infinite interval supplemented with nonlocal boundary conditions containing Riemann-Stieltjes integrals and ω-Riemann-Liouville fractional derivatives of various orders. In the proof of our main results we use the Guo-Krasnosel’skii fixed point theorem and the Leggett-Williams fixed point theorem.

The main goal of this paper is to present a new way of processing a video file using a combination of multiple quantum methods. The design is built upon the novel enhanced quantum representation technique, NEQR, which is then expanded using ideas such as image segmentation, implemented with the help of one or multiple comparators, binarization and cycle shift. This approach allows us to process all frames in parallel according to the desired parameters—one or more thresholds. A demonstration circuit for the proposed design, using a couple of frames, that sums together all the concepts is implemented using the Python programming language and Qiskit open-source framework, made available by IBM. The circuits are analyzed in the experimental section, using the Simulator component and configured using the noise properties of real devices, where we present different relevant metrics obtained by processing the simulation results.

This paper addresses the existence of solutions to a Hadamard fractional differential equation of arbitrary order on an infinite interval, subject to integral boundary conditions that incorporate both Riemann–Stieltjes integrals and Hadamard fractional derivatives. Due to the presence of nontrivial solutions in the associated homogeneous boundary value problem, the problem is classified as resonant. The Mawhin continuation theorem is utilized to derive the main findings.

We explore the existence of solutions for a Hadamard fractional differential equation, subject to nonlocal boundary conditions, which contain Hadamard fractional derivatives and Riemann–Stieltjes integrals. This problem is a resonant one in the sense that the corresponding homogeneous boundary-value problem has nontrivial solutions. In the proof of the main result, we use the Mawhin continuation theorem.

We explore the existence, uniqueness, and multiplicity of positive solutions to a system of Hadamard fractional differential equations that contain fractional integral terms. Defined on a finite interval, this system is subject to general coupled nonlocal boundary conditions encompassing Riemann–Stieltjes integrals and Hadamard fractional derivatives. To establish the main results, we employ several fixed-point theorems, namely the Banach contraction mapping principle, the Schauder fixed-point theorem, the Leggett–Williams fixed-point theorem, and the Guo–Krasnosel’skii fixed-point theorem.

We study the existence and uniqueness of solutions for a system of Hilfer–Hadamard fractional differential equations. These equations are subject to coupled nonlocal boundary conditions that incorporate Riemann–Stieltjes integrals and a range of Hadamard fractional derivatives. To establish our key findings, we apply various fixed point theorems, notably including the Banach contraction mapping principle, the Krasnosel’skii fixed point theorem applied to the sum of two operators, the Schaefer fixed point theorem, and the Leray–Schauder nonlinear alternative.

Our investigation is devoted to examining the existence, uniqueness, and multiplicity of positive solutions for a system of Hadamard fractional differential equations. This system is defined on an infinite interval and is subject to coupled nonlocal boundary conditions. These boundary conditions encompass both Hadamard fractional derivatives and Riemann–Stieltjes integrals, and the nonlinearities within the system are non-negative functions that may not be bounded. To establish the main results, we rely on the utilization of mathematical theorems such as the Schauder fixed-point theorem, the Banach contraction mapping principle, and the Avery–Peterson fixed-point theorem.