7,691 Results Found

In this study, the linear renewal equation is obtained by using the integral equation, the renewal function and the Fourier–Stieltjes transform. It is proven that the linear renewal equation can be obtained by taking the derivative of the integ...

In this paper, under certain condition the Fredholm-Volterra integral equation of the first kind is solved. The existence. and uniqueness of the solution is considered. The Fredholm integral equation of the second kind is established from the work, a...

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L₂(Ω) × C(O, T), Ω = {(x, y) (in) Ω : (sqrt{{x^2}+{y^2}}) ≤ a, z = 0} and T < ∞. The kernel of the Fredholm integral term is considered in the generalize...

In this manuscript we introduce a quadratic integral equation of the Urysohn type of fractional variable order. The existence and uniqueness of solutions of the proposed fractional model are studied by transforming it into an integral equation of fra...

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...

The paper deals with a Volterra integral equation with delay. In order to apply the w-weak generalized contraction theorem for the study of existence and uniqueness of solutions, we rewrite the equation as a fixed point problem. The assumptions take...

Iterative processes are a powerful tool for providing numerical methods for integral equations of the second kind. Integral equations with symmetric kernels are extensively used to model problems, e.g., optimization, electronic and optic problems. We...

This paper studies an irreversible investment problem under a finite horizon. The firm expands its production capacity in irreversible investments by purchasing capital to increase productivity. This problem is a singular stochastic control problem a...

The boundary integral equation defining the interface function for a curved solid/liquid phase transition boundary is analytically solved in steady-state growth conditions. This solution describes dendrite tips evolving in undercooled melts with a co...

We investigate the existence and uniqueness of positive solutions to an integral equation involving convex or concave nonlinearities. A numerical algorithm based on Picard iterations is provided to obtain an approximation of the unique solution. The...

In this study, we consider and analyze an inhomogeneous Whittaker-type differential equation of the form ${\displaystyle \frac{d^{2}y\left(x\right)}{d{x}^2}}+{\displaystyle \frac{1}{x}}{\displaystyle \frac{dy\left(x\right)}{dx}}-{\alpha }^2\left(x^2-{\beta }^2\right)y\left(x\right)=g\left(x\right)$, where $\alpha$ and $\beta$ are given parameters. We investigate the analytical structu...

In this paper, the volume integral equation method (VIEM) is introduced for the analysis of an unbounded isotropic solid composed of multiple isotropic/anisotropic inhomogeneities. A comprehensive examination of a three-dimensional elastostatic VIEM...

In this paper, the integral balance methods of the Stokes’ first equation have been presented. The approximate solution of the fractional Stokes’ first equation using the heat balance integral method has been proposed. The approximate solution of the...

For the impulsive fractional-order system (IFrOS) of order $ϵ\in (1,2)$, there have appeared some conflicting equivalent integral equations in existing studies. However, we find two fractional-order properties of piecewise function and use them...

A symmetric spectral method is applied to investigate the two-dimensional Volterra integral equation with weakly singular kernels and delays. In this work, the solution of the equation we considered is assumed to be sufficiently smooth so that the sp...

The Bagley–Torvik equation (BTE) is an important model in mathematical physics and mechanics, but obtaining its analytical solution remains challenging. For its numerical treatment, the presence of composite functions in the generalized BTE pos...

We investigate a nonlinear integral equation derived through moment approximation from the individual-based representation of spatial logistic dynamics. The equation describes how the densities of pairs of individuals represented by points in continu...

A surface integral equation (SIE) method is applied in order to analyze electromagnetic scattering by bounded arbitrarily shaped three-dimensional objects with the SHDB boundary condition. SHDB is a generalization of SH (Soft-and-Hard) and DB boundar...

The third-order pseudoparabolic equations represent models of filtration, the movement of moisture and salts in soils, heat and mass transfer, etc. Such non-classical equations are often referred to as Sobolev-type equations. We consider an inverse p...

The present paper aims to define three new notions: ${\mathsf{\Theta }}_e$ -contraction, a Hardy–Rogers-type $\mathsf{\Theta }$ -contraction, and an interpolative $\mathsf{\Theta }$ -contraction in the framework of extended b-metric space. Further, some fixed po...

Metric fixed point theory has vast applications in various domain areas, as it helps in finding analytical solutions under various contractive conditions, including non-linear integral-type contractions. In our present work, we have established fixed...

This research paper focuses on investigating the solvability of a constrained problem involving a nonlinear delay functional equation subject to a quadratic functional integral constraint, in two significant cases: firstly, the existence of nondecrea...

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result re...

In this paper, we develop an efficient spectral method for numerically solving the nonlinear Volterra integral equation with weak singularity and delays. Based on the symmetric collocation points, the spectral method is illustrated, and the convergen...

In this paper, the fuzzy Volterra integral equations’ solutions are calculated using a hybrid methodology. The combination of the Elzaki transform and Adomian decomposition method results in the development of a novel regime. The precise fuzzy...

Computational cost tremendously restricts the wide application of conventional integral equation (IE) method in large-scale magnetotelluric (MT) modeling. A couple of obstacles limit the developments of traditional MT modeling based on the IE method....

The current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is defined, continuous, and bounded on the semi...

In this present study, we propose the concept of tricomplex-controlled metric spaces as a generalization of both controlled metric-type spaces and tricomplex metric-type spaces. In this work, we establish fixed point results using Banach, Kannan and...

In this paper, the volume integral equation method (VIEM) is introduced for the numerical analysis of an infinite isotropic solid containing a variety of single isotropic/anisotropic spheroidal inclusions. In order to introduce the VIEM as a versatil...

In this paper, we introduce the notion of neutrosophic rectangular triple-controlled metric space, relaxing the symmetry requirement of neutrosophic metric spaces, by replacing triangular inequalities with rectangular inequalities, and prove fixed po...

Inverse scattering problems (ISPs) stand at the center of many important imaging applications, such as geophysical explorations, industrial non-destructive testing, bio-medical imaging, etc. Recently, a new type of contraction integral equation for i...

Under certain assumptions, the existence of a unique solution of mixed integral equation (MIE) of the second type with a symmetric kernel is discussed, in $L_2\left[\Omega \right]\times C\left[0,T\right],T<1,$$\Omega$ is the position domain of integration and T is the time....

Existence of the solution for the nonlinear quadratic integral equation of the Hammerstein type in the Banach space BC(${\mathbb{R}}_{+}$) has been proved by using the technique of measure of noncompactness and fixed-point theorem. In this article, we obtain an appr...

The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of ($\alpha ,\eta ,\psi$)-contraction in the framework of $\mathfrak{F}$-bipolar...

We consider a two-step numerical approach for solving parabolic initial boundary value problems in 3D simply connected smooth regions. The method uses the Laplace transform in time, reducing the problem to a set of independent stationary boundary val...

This paper proposes an extrapolation method to solve a class of non-linear weakly singular kernel Volterra integral equations with vanishing delay. After the existence and uniqueness of the solution to the original equation are proved, we combine an...

This article concerns the entity of solutions of a quadratic integral equation of the Fredholm type with an altered argument, $x\left(t\right)=p\left(t\right)+x\left(t\right){\int }_0^{1}k(t,\tau )\left(Tx\right)\left(\tau \right)d\tau ,$ where $p,k$...

A set of one-dimensional (as well as one two-dimensional) Fredholm integral equations (IEs) of the first kind of convolution type is solved. The task for solving these equations is ill-posed (first of all, unstable); therefore, the Wiener parametric...

It is common knowledge that studying integral equations accompanied by and related to phase delay is significant, and that significance grows when considering the problem’s time factor. Through this study, one may predict the material’s s...

In this manuscript, we present a novel concept termed graphical ${\Theta }_c$-Kannan contraction within the context of graphically controlled metric-type spaces. Unlike traditional Kannan contraction, this novel concept presents a modified method of contr...

In this paper, we focus on the numerical solution of the second kind of Volterra integral equation with a highly oscillatory Fourier kernel. Based on the calculation of the modified moments, we propose four collocation methods to solve the equations:...

The paper is concerned with the applicability of some new conditions for the convergence of Newton–kantorovich approximations to solution of nonlinear singular integral equation with shift of Uryson type. The results are illustrated in generalized Ho...

The existence of a parametric fractional integral equation and its numerical solution is a big challenge in the field of applied mathematics. For this purpose, we generalize a special type of fixed-point theorems. The intention of this work is to pro...

The electromagnetic interaction between a circular disk with finite conductivity and finite thickness and a coaxial circular loop of constant current is addressed here. The finite conductivity and thickness of the material disk lead to the adoption o...

The present work investigates the spatial evolution characteristics of solutions to the Moore–Gibson–Thompson heat equation within a three-dimensional cylindrical geometry. By constructing an integral-differential inequality framework, we...

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and unique...

The widespread of composite structures demands efficient numerical methods for the simulation dynamic behaviour of elastic laminates with interface delaminations with interacting faces. An advanced boundary integral equation method employing the Hank...

In this paper, we devised an analytical technique to efficiently evaluate the improper integrals of oscillating and slowly decaying functions arising from the application of the method of analytical preconditioning (MAP) to a spectral-domain integral...

In this study, the extended (3 + 1)-dimensional Jimbo–Miwa equation, which has not been previously studied using Lie symmetry techniques, is the focus. We derive new symmetry reductions and exact invariant solutions, including lump and rogue wa...

In this paper, we investigate the existence of positive solutions of the eigenvalue problem for a singular tempered fractional equation with a Riemann–Stieltjes integral boundary condition and signed measures. By establishing the Green function...