In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

In the present paper we give a fractional generalization of the Lauwerier formulation of the boundary value problem of the temperature field in oil strata. The Caputo fractional derivative operator and the Laplace transform are the important tools for solving the proposed problem. By using Efros’ theorem which is a modified form of convolution theorem for Laplace transform, the solution is obta...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that ...

We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n×n Hermitian matrices as n → ∞. Assuming that the test function of statistics is smooth enough and using the asymptotic formulas by Deift et al for orthogonal polynomials with varying weights, we show first that if the support of the Density of States of ...

In this paper we have studied the combination of Elzaki and Laplace transforms to produce a degenerative new double integral transform, transform called Elzaki-Laplace (ELT), then applied it some partial differential equations find its exact solution.

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on ...

Continuous-time quantum walk (CTQW) on a given graph is investigated by using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with the graph. It is shown that, the probability amplitude of observing the CTQW at a given site at time t is related to the inverse Laplace transformation of t...

In the discrete-time supercritical branching random walk there is a Kesten-Stigum type result for the martingales formed by the Laplace transform of the nth generation positions. Roughly, this says that for suitable values of the argument of the Laplace transform the martingales converge in mean provided an X log X condition holds. Here it is established that when this moment condition fails, s...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that ...