Inclusion and Neighborhood on a Multivalent q-Symmetric Function with Poisson Distribution Operators by Ebrahim Amini, Shrideh Al-Omari, Dayalal Suthar

“…Then, by utilizing the Poisson distribution and the concept of the q-analogue Salagean integral operator, the p-valent convergence polynomial was introduced. …”
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A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension by G. Muchatibaya, S. Fassari, F. Rinaldi, J. Mushanyu

“…The ground state energy E0(λ) of Hλ=-d2/dx2-λe-x2 is computed for small values of λ by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which ϵ0(λ)=|E0(λ)|1/2 is the root.…”
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Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces by Yanqi Yang, Shuangping Tao

“…Let T be the singular integral operator with variable kernel defined by Tf(x)=p.v.…”
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The formal Laplace-Borel transform of Fliess operators and the composition product by Yaqin Li, W. Steven Gray

“…The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. …”
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On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions by Xiaobin Wang, Muhammad Shoaib Saleem, Kiran Naseem Aslam, Xingxing Wu, Tong Zhou

“…The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of h-convex function. …”
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$R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission by Toshikazu Kuniya, Mimmo Iannelli

“…We show that the spectral radius of the Fréchet derivative of a nonlinear integral operator plays the role of a threshold value for the global behavior of the model, that is, if the value is less than unity, then the disease-free steady state of the model is globally asymptotically stable, while if the value is greater than unity, then the model has a unique globally asymptotically stable endemic (nontrivial) periodic solution. …”
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Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform by Hafte Amsalu Kahsay, Adnan Khan, Sajjad Khan, Kahsay Godifey Wubneh

“…In this paper, our leading objective is to relate the fractional integral operator known as Pδ-transform with the ք-extended Mathieu series. …”
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Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable by Najla M. Alarifi, Rabha W. Ibrahim

“…We deal with a fractional integral operator type Prabhakar operator in the open unit disk. …”
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Certain New Class of Harmonic Functions Involving Quantum Calculus by Mohammad Faisal Khan

“…Here in this paper, we are using the concepts of q-calculus operator theory associated with harmonic functions and define the q-Noor integral operator for harmonic functions f∈H0. We investigate a new class SH0m,q,α of harmonic functions f∈H0. …”
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Exciting Fixed Point Results on a Novel Space with Supportive Applications by Hasanen A. Hammad, Hassen Aydi, Yaé Ulrich Gaba

“…Moreover, we apply the theoretical results to find a unique solution of a complex valued Atangana-Baleanu fractional integral operator and a system of complex linear equations. …”
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Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations by Sohrab Bazm, Fatemeh Pahlevani

“…One significant advantage of this method lies in its ability to avoid the need for direct integration to discretize the integral operator. Error estimates are provided and two illustrative examples are included to demonstrate the method’s effectiveness and practical applicability.…”
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Problems solving in the integral calculus and the determination of the area under the curve by Juan E. N´apoles Vald´es, Maria Nubia Quevedo

“…This article presents a useful problem for Mathematics Education, derived from a generalized integral operator, for this we define what we understand by an integrable function in this generalized sense, and the geometric interpretation of a generalized definite integral is presented. …”
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Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses by Hasanen A. Hammad, Manuel De la Sen

“…Employing the Atangana–Baleanu–Caputo (ABC) derivative, we transform the system into an equivalent fixed-point (FP) problem through an integral operator. Subsequently, the Bohnenblust–Karlin FP theorem is leveraged to establish existence results. …”
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Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments by Jianping Wang, Shujing Gao, Yueli Luo, Dehui Xie

“…It is shown that the global dynamics are determined by the basic reproduction number R0 which is defined through the spectral radius of a linear integral operator. If R0 < 1, then the disease-free periodic solution is globally asymptotically stable and if R0 > 1, then the disease persists. …”
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The Hölder and Minkowski Inequalities Utilizing a Fractional Operator Involvement of Pseudo-Operator by Hadiseh Fallah Andevari, Azizollah Babakhani, Daniela Oliveira

“…A generalized integral operator of order $\alpha$ of a real function $f$  including a parameter set $P$, namely $K_P^\alpha f(t)$ has been introduced by O. …”
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Numerical Investigation of Fractional-Order Differential Equations via φ-Haar-Wavelet Method by F. M. Alharbi, A. M. Zidan, Muhammad Naeem, Rasool Shah, Kamsing Nonlaopon

“…In this paper, we derived an explicit formula for the φ-fractional integral of the Haar-wavelet by utilizing the φ-fractional integral operator. We also extended our method to nonlinear φ-FDEs. …”
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Integral representation of vertical operators on the Bergman space over the upper half-plane by Bais, Shubham R., Venku Naidu, D., Mohan, Pinlodi

“…In this article, we prove that every vertical operator on the Bergman space $\mathcal{A}^2(\Pi )$ over the upper half-plane can be uniquely represented as an integral operator of the form \begin{equation*} \left(S_\varphi f\right)(z) = \int _{\Pi } f(w) \varphi (z-\overline{w}) d\mu (w),~~\forall f\in \mathcal{A}^2(\Pi ),~z\in \Pi , \end{equation*} where $\varphi $ is an analytic function on $\Pi $ given by \begin{equation*} \varphi (z) = \int _{\mathbb{R}_+}\xi \sigma (\xi ) e^{iz\xi } d\xi , \ \forall z\in \Pi \end{equation*} for some $\sigma \in L^\infty (\mathbb{R}_+)$. …”
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μ Robust Stable Extrapolation of a Stationary Random Process with Interval Limited Variance by Igor G. Sidorov

“…This approach, unlike others (for example, probabilistic), always ensures the existence of a stable result and solution of a single optimum in the problem of interval minimax extrapolation due to regularization by a small parameter with a derivative of the eigenfunction of a singularly perturbed integro-differential equation of the first order with an integral operator of the Voltaire type of the second kind, defined by a symmetric, closed real the core. …”
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Further Developments of Bessel Functions via Conformable Calculus with Applications by Mahmoud Abul-Ez, Mohra Zayed, Ali Youssef

“…We establish several important formulas of the fractional Laplace Integral operator acting on the CFBFs of the first kind. …”
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P-FFT Accelerated EFIE with a Novel Diagonal Perturbed ILUT Preconditioner for Electromagnetic Scattering by Conducting Objects in Half Space by Lan-Wei Guo, Yongpin Chen, Jun Hu, Joshua Le-Wei Li

“…Inspired by the idea of the improved electric field integral operator (IEFIO), the geometrical-optics current/principle value term of the magnetic field integral equation is used as a physical perturbation to stabilize the traditional ILUT perconditioning matrix. …”
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