In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. T...

For d-dimensional Lévy models we provide a method for Finite Element-based asset pricing. We derive the partial integrodifferential pricing equation and prove that the corresponding variational problem is well-posed. Hereto, an explicit characterization of the domain of the bilinear form is given. For the numerical implementation the problem is discretized by sparse tensor product Finite Elemen...

Correlation functions of exactly solvable models can be described by differential equations [1]. In this paper we show that for non free fermionic case differential equations should be replaced by integro-differential equations. We derive an integro-differential equation, which describes time and temperature dependent correlation function 〈ψ(0, 0)ψ(x, t)〉T of penetrable Bose gas. The integrodif...

In this paper, we establish the existence and uniqueness results to Cauchy problem posed for a fuzzy fractional Volterra-Stieltjes integrodifferential equation. The method of successive approximations is used prove existence, whereas contraction theory applied solution problem.