Foundations, Volume 2, Issue 1

There is little doubt that life’s origin followed from the known physical and chemical laws of Nature. The most general scientific framework incorporating the laws of Nature and applicable to most known processes to good approximation, is that...

The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag–Leffler function and two H-functions. The resulting integral formulas are described in terms of the H-function of severa...

A coupled system of Hilfer fractional differential inclusions with nonlocal integral boundary conditions is considered. An existence result is established when the set-valued maps have non-convex values. We treat the case when the set-valued maps are...

We utilize relativistic quantum mechanics to develop general quantum field-theoretic foundations suitable for understanding, analyzing, and designing generic quantum antennas for potential use in secure quantum communication systems and other applica...

The local convergence of a generalized $(p+1)$-step iterative method of order $2p+1$ is established in order to estimate the locally unique solutions of nonlinear equations in the Banach spaces. In earlier studies, convergence analysis for the given iter...

We study semi-local convergence of two-step Jarratt-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis we use the approach of restricted convergence regi...

We analyze Molecular Hydrogen Ions (MHIs) formed by collisions of low-energy protons with the Second Flavor of Hydrogen Atoms SFHA, whose existence was previously proven by two kinds of atomic experiments and also evidenced by two kinds of astrophysi...

In the framework of the effective mass approximation, negative and positive trions, exciton, and biexciton states are investigated in strongly prolate ellipsoidal quantum dots by the variational method. Since the ellipsoidal quantum dot has a prolate...

Rigorous peer-reviews are the basis of high-quality academic publishing [...]

In this paper, fractional Lyapunov functions for epidemic models are introduced and the concept of Mittag-Leffler stability is applied. The global stability of the epidemic model at an equilibrium state is established.

Vector-valued electromagnetic waves for which the integral of the electric field over time is zero at every location in space were characterized as “usual” by Bessonov several decades ago. Otherwise, they were called “strange”...

In the review, based on the analysis of the results published in the works of domestic and foreign researchers, a variant of an unconventional interpretation of the photoluminescence of dispersive media in the energy range of 0.5–3 eV is propos...

Quadratic integral equations of fractional order have been studied from different views. Here we shall study the existence of continuous solutions of a $\varphi -$ fractional-orders quadratic functional integral equation, establish some properties...

In this paper, we look at the two-point boundary value problem for a finite nabla fractional difference equation with dual non-local boundary conditions. First, we derive the associated Green’s function and some of its properties. Using the Guo...

We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis, we use the approach of restricted converge...

In this work, we present a Big Rip scenario within the framework of the generalized Brans-Dicke (GBD) theory. In the GBD theory, we consider an evolving BD parameter along with a self-interacting potential. An anisotropic background is considered to...

The celebrated Traub’s method involving Banach space-defined operators is extended. The main feature in this study involves the determination of a subset of the original domain that also contains the Traub iterates. In the smaller domain, the L...

Previously published analytical results for the effects of a high-frequency laser field on hydrogen Rydberg atoms demonstrated that the unperturbed elliptical orbit of the Rydberg electron, generally is engaged simultaneously in the precession of the...

A new $\alpha$-emitting ²¹⁴U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even–even neutron deficient ^214,216,218U isotopes and to examine $\alpha$...

An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonl...

This current work is devoted to develop qualitative theory of existence of solution to some families of fractional order differential equations (FODEs). For this purposes we utilize fixed point theory due to Banach and Schauder. Further using differe...

Many totally different kinds of astrophysical observations demonstrated that, in our universe, there exists a preferred direction. Specifically, from observations in a wide range of frequencies, the alignment of various preferred directions in differ...