Results 21 to 30 of about 316,882 (148)
Soliton Equations Extracted from the Noncommutative Zero-Curvature Equation [PDF]
Prog.Theor.Phys. 105 (2001) 1045-1057, 2001 We investigate the equation where the commutation relation in 2-dimensional zero-curvature equation composed of the algebra-valued potentials is replaced by the Moyal bracket and the algebra-valued potentials are replaced by the non-algebra-valued ones with two more new variables.
arxiv +1 more source
On Some Operators Involving Hadamard Derivatives [PDF]
, 2013 In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or Hyper-Bessel-type operators.
Garra, Roberto, Polito, Federico
core +1 more source
Analysis of stability for stochastic delay integro-differential equations
Journal of Inequalities and Applications, 2018 In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step ...
Yu Zhang, Longsuo Li
doaj +1 more source
Hypergeometric solutions to Schrödinger equations for the quantum Painlevé equations [PDF]
, 2011 We consider Schr\"odinger equations for the quantum Painlev\'e equations. We present hypergeometric solutions of the Schr\"odinger equations for the quantum Painlev\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\"odinger equations for the quantum Painlev\'e equations and ...
arxiv +1 more source
, 1997 Correlation functions of exactly solvable models can be described by differential equation [Barough, McCoy, Wu]. In this paper we show that for non free fermionic case differential equations should be replaced by integro-differential equations.
Kojima, T., Korepin, V., Slavnov, N.
core +2 more sources
A study on the bilinear equation of the sixth Painlevé transcendents [PDF]
arXiv, 2023 The sixth Painlev\'e equation is a basic equation among the non-linear differential equations with three fixed singularities, corresponding to Gauss's hypergeometric differential equation among the linear differential equations. It is known that 2nd order Fuchsian differential equations with three singular points are reduced to the hypergeometric ...
arxiv
Front motion for phase transitions in systems with memory
, 2000 We consider the Allen-Cahn equations with memory (a partial integro-differential convolution equation). The prototype kernels are exponentially decreasing functions of time and they reduce the integrodifferential equation to a hyperbolic one, the damped ...
Aizicovici +17 more
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Solving the Integral Differential Equations with Delayed Argument by Using the DTM Method
Sensors, 2022 Recently, a lot of attention has been paid to the field of research connected with the wireless sensor network and industrial internet of things. The solutions found by theorists are next used in practice in such area as smart industries, smart devices ...
Edyta Hetmaniok +2 more
doaj +1 more source
Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media
, 2011 We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order.
A. A. Kilbas +15 more
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Convolution-type derivatives, hitting-times of subordinators and time-changed $C_0$-semigroups [PDF]
, 2014 In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by means of convolution-type integro-differential operators similar to the ...
AI Saichev +29 more
core +1 more source