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

“…Subsequently, the Bohnenblust–Karlin FP theorem is leveraged to establish existence results. …”
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The Meijer transformation of generalized functions by E. L. Koh, E. Y. Deeba, M. A. Ali

“…This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.…”
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Practically effective adjustment variable selection in causal inference by Atsushi Noda, Takashi Isozaki

“…We also present and prove a theorem on causal effect computation possibility in CPDAGs. …”
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Positive Solutions for Some Competitive Fractional Systems in Bounded Domains by Imed Bachar, Habib Mâagli, Noureddine Zeddini

“…Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some Dirichlet conditions, where 0<α<2, σ,β≥1,s,r≥0. …”
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Composite trapezoidal quadrature for computing hypersingular integrals on interval by Xiaoping Zhang, Jin Li

“…At last, several examples were presented to test our theorem.…”
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Arcadia (1993) de Tom Stoppard : la passion du bilan by Nicole Boireau

“…Based on a fake love affair, on a literary enigma and on the illusory solution of Fermat’s theorem, Tom Stoppard’s Arcadia takes place in an imaginary estate which, like a palimpsest bears the marks of stylistic changes. …”
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Null Controllability of a Four Stage and Age-Structured Population Dynamics Model by Amidou Traoré, Bedr’Eddine Ainseba, Oumar Traoré

“…Our method combines fixed point theorem and Carleman estimate. We end this work with numerical illustrations.…”
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Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative by Fareeha Sami Khan, M. Khalid, Omar Bazighifan, A. El-Mesady

“…Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s stability in Banach space. …”
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Antenna Array Design in MIMO Radar Using NSK Polynomial Factorization Algorithm by Shuainan Gu, Ke Li, Xiukun Ren, Na-e Zheng

“…First, linear factors are extracted by extended Vieta theorem. Then, undermined high-order factors are confirmed with Newton interpolation and certain high-order factors should be searched for within the undermined ones. …”
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Approximation of Bivariate Functions via Smooth Extensions by Zhihua Zhang

“…Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. …”
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Existence and construction of the Peano selection for a multivalued function by Rosario D. Delgado V., Waymer A. Barreto V., Teodoro L. Acevedo T.

“…Finally, using the General Theorem of multivalued functions, the necessary conditions are determined for the multivalued function, F : [0, 1]-->[0, 1] × [0, 1] to admit the construction of the selection of Peano.…”
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Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition by Imed Bachar, Habib Mâagli, Hassan Eltayeb

“…Based on the Banach fixed point theorem on an appropriate space, we prove that this problem possesses a unique continuous solution u satisfying ut≤cωt,for t∈0,1 and c>0, where ωt≔tα−21−t2.…”
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Analysis of an Impulsive One-Predator and Two-Prey System with Stage-Structure and Generalized Functional Response by Xiangmin Ma, Yuanfu Shao, Zhen Wang, Xianjia Fang, Zhenguo Luo

“…Sufficient conditions for the permanence of this system are established via impulsive differential comparison theorem. Furthermore, abundant results of numerical simulations are given by choosing two different and concrete functional responses, which indicate that impulsive effects, stage-structure, and functional responses are vital to the dynamical properties of this system. …”
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On a class of second-order impulsive boundary value problem at resonance by Guolan Cai, Zengji Du, Weigao Ge

“…By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. …”
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Existence of Solutions for Boundary Value Problem of a Caputo Fractional Difference Equation by Zhiping Liu, Shugui Kang, Huiqin Chen, Jianmin Guo, Yaqiong Cui, Caixia Guo

“…We use Schauder fixed point theorem to deduce the existence of solutions. The proofs are based upon the theory of discrete fractional calculus. …”
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Optimal investment and reinsurance for the insurer and reinsurer with the joint exponential utility by Wuyuan Jiang, Zechao Miao, Jun Liu

“…By solving the HJB equation, we obtain the optimal investment-reinsurance strategies, and present the proof of the verification theorem. Finally, we demonstrate a numerical analysis, and the economic implications of our findings are illustrated.…”
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A brief functional investigation via Sobolev spaces to analyze the behavior of Oseen flow in external domains by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales, Alice Rosa da Silva

“… This work serves as an introductory exploration of Oseen flow, a mathematical and physical framework for modeling fluid dynamics, with a specific focus on viscous substances like liquids or gases. The presented theorem and its associated lemmas are an extension of the foundational theory of potential flow, which is conventionally applied to inviscid fluids. …”
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Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations by Yige Zhao, Shurong Sun, Zhenlai Han, Qiuping Li

“…By the properties of the Green function and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation boundary value problem are considered, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. …”
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A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications by Zhongping Wan, Jia-Wei Chen, Hai Sun, Liuyang Yuan

“…As an application, the strong convergence theorem for a class of bilevel variational inequalities is derived in Hilbert space. …”
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Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function by Jie Wen, Yuanhao Shi, Xiaonong Lu

“…The stabilization of a Rotary Inverted Pendulum based on Lyapunov stability theorem is investigated in this paper. The key of designing control laws by Lyapunov control method is the construction of Lyapunov function. …”
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