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Analysis of Volterra Integrodifferential Equations with the Fractal-Fractional Differential Operator
Complexity, 2023 In this paper, a class of integrodifferential equations with the Caputo fractal-fractional derivative is considered. We study the exact and numerical solutions of the said problem with a fractal-fractional differential operator.
null Kamran +5 more
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On the Expected Discounted Penalty Function Using Physics-Informed Neural Network
Journal of Mathematics, 2023 We study the expected discounted penalty at ruin under a stochastic discount rate for the compound Poisson risk model with a threshold dividend strategy. The discount rate is modeled by a Poisson process and a standard Brownian motion.
Jiayu Wang, Houchun Wang
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Advances in Difference Equations, 2010 We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus ...
John A. D. Appleby
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Nonlinear Engineering, 2023 In this study, a numerical approach is presented to solve the linear and nonlinear hyperbolic Volterra integrodifferential equations (HVIDEs). The regularization of a Legendre-collocation spectral method is applied for solving HVIDE of the second kind ...
Mirzaei G. F., Rostamy Davood
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Hyperbolic integrodifferential equations [PDF]
Proceedings of the American Mathematical Society, 1975 Hyperbolic integrodifferential equations are defined and conditions sufficient for hyperbolicity are given. The theory includes that of constant coefficient hyperbolic partial differential equations. Other examples are given.
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Journal of Function Spaces, 2023 In the present paper, a new efficient technique is described for solving nonlinear mixed partial integrodifferential equations with continuous kernels.
Abeer M. Al-Bugami +2 more
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Nonlinear Volterra Integrodifferential Equations
Journal of Mathematical Analysis and Applications, 1994 This is a continuation of the authors' earlier paper [J. Math. Anal. Appl. 139, No. 1, 78-109 (1989; Zbl 0681.45010)]. Consider the semilinear Volterra integro-differential equation \[ u'(t) + Au(t) = \int^ t_ 0 a(t,s)g \bigl( s,u(s) \bigr) ds + f \bigl( t,u(t) \bigr), \quad t > 0, \] with \(u(0) = u_ 0\), where \(-A\) generates an analytic semigroup ...
Heard, M.L., Rankin, S.M.
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Abstract and Applied Analysis, 2014 We consider a compound Poisson risk model with dependence and a constant dividend barrier. A dependence structure between the claim amount and the interclaim time is introduced through a Farlie-Gumbel-Morgenstern copula.
Donghai Liu, Zaiming Liu, Dan Peng
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Solving Fuzzy Volterra Integrodifferential Equations of Fractional Order by Bernoulli Wavelet Method
Advances in Fuzzy Systems, 2018 A matrix method called the Bernoulli wavelet method is presented for numerically solving the fuzzy fractional integrodifferential equations. Using the collocation points, this method transforms the fuzzy fractional integrodifferential equation to a ...
R. Mastani Shabestari +2 more
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Abstract and Applied Analysis, 2012 The reproducing kernel method (RKM) and the Adomian decomposition method (ADM) are applied to solve nth-order nonlinear weakly singular Volterra integrodifferential equations. The numerical solutions of this class of equations have been a difficult topic
Xueqin Lv, Sixing Shi
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