In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

There is a whole range of emergent phenomena in non-equilibrium behaviors can be well described by a set of stochastic differential equations. Inspired by an insight gained during our study of robustness and stability in phage lambda genetic switch in modern biology, we found that there exists a classification of generic nonequilibrium processes: In the continuous description in terms of stocha...

this article is devoted to the study of existence and multiplicity of positive solutions to aclass of nonlinear fractional order multi-point boundary value problems of the type−dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where dq0+ represents standard riemann-liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ∞...

This paper considers random Hill’s equations in the limit where the periodic forcing function becomes a Dirac delta function. For this class of equations, the forcing strength qk, the oscillation frequency λk, and the period (∆τ)k are allowed to vary from cycle to cycle. Such equations arise in astrophysical orbital problems in extended mass distributions, in the reheating problem for inflation...

This study proposes a two-phase, algebraic approach to resolve the rotation cycle time and number of shipments for a multi-item, economic production quantity (EPQ) model with a random defective rate. A conventional method for solving a multi-item EPQ model is to use differential calculus and Hessian matrix equations on system cost function to prove convexity first and then derive an optimal pro...

We obtain oscillation criteria for a second order self-adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function. We illustrate our results with some nontrivial examples.

The limit cycles of nonlinear systems under the small stochastic disturbances are considered. The random trajectories of forced system leave the deterministic cycle and form some stochastic bundle around it. The probabilistic description of this bundle near cycle based on stochastic sensitivity function (SSF) is suggested. The SSF is a covariance matrix for periodic solution of linear stochasti...