Foundations, Volume 2, Issue 4

It is known that, from a modeling point of view, fractional dynamic equations are more suitable compared to integer derivative models. In fact, a fractional dynamic equation is referred to as an equation with memory. To demonstrate that the fractiona...

The evolution of the atmospheric temperature in the past, resulted from the EPICA project (European Project for Ice Coring in Antarctica) for the analysis of air bubbles in ice deposits near three weather stations in Antarctica, includes several glac...

It is well known that HIV (human immunodeficiency virus) weakens the immune system of individuals, resulting in risk of other infections, such as pneumonia. The most frequent viral pneumonia seen in individuals infected with HIV is cytomegalovirus (C...

A psychology experiment examining decision-making on a continuum of subjectively equivalent alternatives (directions) revealed that subjects follow a common pattern, giving preference to just a few directions over all others. When restricted experime...

This paper highlights 20 significant problems in AI research, with potential solutions via the SP Theory of Intelligence (SPTI) and its realisation in the SP Computer Model. With other evidence referenced in the paper, this is strong evidence in supp...

We compare the convergence balls and the dynamical behaviors of two efficient weighted-Newton-like equation solvers by Sharma and Arora, and Grau-Sánchez et al. First of all, the results of ball convergence for these algorithms are established...

We propose the semi-local convergence of two derivative-free, competing methods of order six to address non-linear equations. The sufficient convergence criteria are the same, making a direct comparison between them possible. The existing convergence...

An innovative and integrative modeling strategy for assessing the sustainability and resilience of social-ecological systems (SES) is presented by introducing a social-ecological entropy production (SEEP) method. In analogy to the thermodynamic entro...

This interdisciplinary work communicates the identification and quantification of elements responsible for the bioactive potency of leaves from pointed gourd, trichosanthes dioica, using laser-induced breakdown spectroscopy (LIBS). Calibration-free L...

This article reviews the electrodynamic force law of Wilhelm Weber and its importance in electromagnetic theory. An introduction is given to Weber’s force and it is shown how it has been utilised in the literature to explain electromagnetism as...

This work investigates spatial and temporal distributions of hydroxyl, OH, in laser-plasma in laboratory air at standard ambient temperature and pressure. Of interest are determination of temperature and density of OH and establishment of a correlati...

This paper is concerned with the existence of solutions for a new boundary value problem of nonlinear coupled $(k,\psi )$–Hilfer fractional differential equations subject to coupled $(k,\psi )$–Riemann–Liouville fractional integral boun...

The proton radius puzzle is one of the most fundamental challenges of modern physics. Before the year 2010, the proton charge radius r_p was determined by the spectroscopic method, relying on the electron energy levels in hydrogen atoms, and by the el...

The present study is focused on revealing a characteristic kink of the neutron shell closure N = 126 across the Hg-isotopic chain within the relativistic mean-field (RMF) approach with the IOPB-I, DD-ME2, DD-PC1 and NL3 parameter sets. The RMF densit...

We construct a Green’s function for the three-term fractional differential equation $-D_{0+}^{\alpha }u+a{D}_{0^{+}}^{\mu }u+f\left(t\right)u=h\left(t\right)$, $0<t<b$, where $\alpha \in (2,3]$, $\mu \in (1,2]$, and f is continuous, satisfying the boundary conditions $u\left(0\right)=u^{\&}$...

In this paper, we treat some fractional differential equations on the sequence Lebesgue spaces ${\ell }^p\left({\mathbb{N}}_0\right)$ with $p\ge 1$. The Caputo fractional calculus extends the usual derivation. The operator, associated to the Cauchy problem, is defined by a conv...

The double nature of material particles, i.e., their wave and corpuscular characteristics, is usually considered incomprehensible, as it cannot be represented visually. It is proposed to the student, in introductory courses, as a fact justified by qu...

We consider a predictor–corrector numerical method for solving Caputo–Hadamard fractional differential equation over the uniform mesh $\log t_j=\log a+\left(\log \frac{t_N}{a}\right)\left(\frac{j}{N}\right),j=0,1,2,\dots ,N$ with $a\ge 1$, where $\log a=\log t_0<\log t_1<\dots <\log t_N=\log T$...

The semi-local convergence is presented for a one parameter seventh order method to obtain solutions of Banach space valued nonlinear models. Existing works utilized hypotheses up to the eighth derivative to prove the local convergence. But these hig...