161,564 Results Found

There is a fairly widespread belief that the problem of existence is not an essential issue for logic. Logic, though formal, must deal with the problem of existence. However, logic should be limited to describing “formal existence” or &ld...

“water origin theory” (WOT) in the world is defined the water as a kind of original medium creating and covering the world. The properties of the water in these WOTs are very similar to the non-existence, The “water” in these WOTs is the most primord...

I considered the problem of existence of virtual objects, mainly the mode of existence of these objects, while I omitted the issue of the criteria of their existence. I present a brief exposition of alternative the concepts of modes (forms, kinds) of...

The process of human understanding of the world starts from viewing complex chaos, proceeding to monism followed by the contradiction theory, and finally returning to complexity theory, but without giving up the pursuit of monism. Lao-Tzu and Heracli...

In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermo...

Reflecting on the history of discussions about the existence of mathematics, we can summarize the characteristics of the traditional path of research on the existence of mathematics. By analyzing the drawbacks of traditional research on the existence...

Uganda is richly endowed with flora and fauna. Until the early 2000s, most of the types of vegetation have remained natural/virgin forests and shrubs until recent years, when human activities have damaged them. Understanding the different ways that p...

This paper investigates how abstracta, such as numbers or functions, can be said to emerge at particular times, as in the claim that “complex numbers did not exist before the sixteenth century.” Standard accounts encounter well-known diff...

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness...

In the real world, the indeterminate phenomenon and determinate phenomenon are symmetric; however, the indeterminate phenomenon absolutely exists. Hence, the indeterminate dynamic phenomenon is studied in this paper by using uncertainty theory, where...

This paper deals with the study of the existence and non-existence of solutions of a three-parameter family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$ -Riemann-Liouville f...

Herein, we mainly employ the fixed point theorem and Lax-Milgram theorem in functional analysis to prove the existence and uniqueness of generalized and mixed finite element (MFE) solutions for two-dimensional steady Boussinesq equation. Thus, we can...

In this paper, I examine Aristotle’s cosmological proof of God’s existence, Avicenna’s metaphysical proof, and Thomas Aquinas’s five-way proof. By comparing these proofs, I argue that philosophers and theologians take differen...

In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasin...

This work presents a new approach that aims to characterize the spatio-temporal relationships that exist between geographical objects that are absent or non-existent at the moment of analysis. First, we would like to propose a formal analysis of the...

Anselm’s argument for the existence of God posits that the concept of God inherently implies its existence. Tang Junyi critiques this argument from two fundamental angles. Firstly, he argues that the contingency of human thought places an unwar...

Analogous to Kolmogorov’s theorem for the existence of stochastic processes describing random functions, we consider theorems for the existence of stochastic processes describing random measures as limits of inverse measure systems. Specificall...

In this paper, we provide existence and uniqueness results for the initial value problems associated with mixed Riemann–Liouville/Caputo differential equations in the real domain. We show that, under appropriate conditions in a fractional order...

We study the existence/uniqueness of conformable fractional type impulsive nonlinear systems as well as the controllability of linear/semilinear conformable fractional type impulsive controlled systems. Using the conformable fractional derivative app...

In this work, we study the global existence of solutions reaction-diffusion systems with control of mass on multiple domains. Some of these domains overlap, and as a result, an unknown defined on one subdomain can impact another unknown defined on a...

We show the existence of at least one nontrivial solution for a nonlinear sixth-order ordinary differential equation is investigated. Our approach is based on critical point theory.

Classical periodic solution theories of undamped Duffing equations are mostly restricted to continuous nonlinearities, while discontinuous models from mechanical impact and switching circuits lack systematic existence criteria for crossing periodic o...

In this paper, we study the existence and uniqueness of second-order impulsive delay differential systems. Firstly, we define cosine-type and sine-type delay matrix functions, which are used to derive the solutions of the impulsive delay differential...

One of the key applications of the Caputo fractional derivative is that the fractional order of the derivative can be utilized as a parameter to improve the mathematical model by comparing it to real data. To do so, we must first establish that the s...

This manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing $\Psi$-Caputo fractional derivatives. The application of Banach’s fixed-point theorem (BFPT) ensures t...

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets....

The aim of this article is to show how and in what stages G. W. Leibniz came to develop his proof of God’s existence from eternal truths. It begins by tracing the main stages in the history of this proof, initially forged by Augustine of Hippo,...

This paper is concerned with the existence of positive solutions to the fourth-order boundary value problem $u^{\left(4\right)}\left(x\right)=f(x,u\left(x\right),u^{″}\left(x\right))$ on the interval [0, 1] with the boundary condition $u\left(0\right)=u\left(1\right)=u^{″}\left(0\right)=u^{″}\left(1\right)=0,$ which models a staticall...

This paper investigates the existence, uniqueness, and finite-time stability of solutions to a class of nonlinear systems governed by the Hadamard fractional derivative. The analysis is carried out using two fundamental tools from fixed point theory:...

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove t...

This research investigates laser-induced convection through a stream function-vorticity formulation. Specifically, this paper considers a solution to the steady Boussinesq Navier–Stokes equations in two dimensions with a slip boundary condition...

In the theory of differential equations, the study of existence and the uniqueness of the solutions are important. In the last few decades, many researchers have had a keen interest in finding the existence–uniqueness solution of constant fract...

The main purpose of this study was to demonstrate the existence and the uniqueness theorem of the solution of the neutral stochastic differential equations under sufficient conditions. As an alternative to the stochastic analysis theory of the neutra...

In this paper, we study the existence and uniqueness of solutions for nabla fractional systems. By using the properties of bijective functions, we obtain a necessary and sufficient condition ensuring the existence and uniqueness of solutions for a cl...

In this article, we investigate the existence of a nontrivial solution for the nonlinear Choquard equation with upper critical exponent see Equation (6). The Riesz potential in this case has never been studied. We establish the existence of the groun...

Fractional differential beam type equations are considered. By using an efficient approach, we prove the existence and uniqueness of continuous solutions. An iterative scheme for approximating the solution is given. Some examples are presented.

The aim of this work is to study a class of nabla fractional difference equations with anti-periodic conditions. First, we construct the related Green’s function. After deducing some of its useful properties, we obtain an upper bound for its su...

In this paper, we investigate a reaction–diffusion equation with a Caputo fractional derivative in time and with boundary conditions. According to the principle of contraction mapping, we first prove the existence and uniqueness of local soluti...

In this paper, we prove the existence and uniqueness of solution for some Riemann–Liouville fractional nonlinear boundary value problems. The positivity of the solution and the monotony of iterations are also considered. Some examples are prese...

Fractional stochastic differential equations are still in their infancy. Based on some existing results, the main difficulties here are how to deal with those equations if the fractional order is varying with time and how to confirm the existence of...

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...

In this paper, a new structure of an applied model of thermostat is defined using the generalized $\psi$-operators with three-point boundary conditions. Some useful properties of the relevant Green’s function are established, and based on these...

Conditions under which compositions of component systems form a well-defined system-of-systems are here formulated at a fundamental level. Statement of what defines a well-defined composition and sufficient conditions guaranteeing such a result offer...

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carathéodory-type mu...

This manuscript investigates the existence, uniqueness, and different forms of Ulam stability for a system of three coupled differential equations involving the Riemann–Liouville (RL) fractional operator. The Leray–Schauder alternative is...

This study establishes the existence and stability of solutions for a general class of Riemann–Liouville (RL) fractional differential equations (FDEs) with a variable order and finite delay. Our findings are confirmed by the fixed-point theorem...

Sensors and sensor networks have become widespread in today’s technological world. As with any technical system, sensors and sensor networks face certain challenges, one of which is the problem of energy efficiency, the solution of which allows...

Fractional multi-delay differential systems, as an important mathematical model, can effectively describe viscoelastic materials and non-local delay responses in ecosystem population dynamics. It has a wide and profound application background in inte...

In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties. Then, we impose some...

In this paper, we investigate the Cauchy problem for nonautonomous abstract evolution equations of the form $y^{\prime }\left(t\right)=A\left(t\right)y\left(t\right)+f(t,y\left(t\right)),t\ge 0$, $y\left(0\right)=y_0$. We obtain new existence theorems for global mild solutions under both compact and noncompact e...