In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations and extension of this type of integral equations. The result is obtained by using the  coupled fixed point theorems in the framework of Banach space $ X=C([a,b],mathbb{R})$. Finally, we  give an example to illustrate the applications of our results.

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

The present investigation is concerned with the role of bottom slope in the stability properties of two-dimensional disturbances in sheared two-layer immiscible fluids with stepwise densities. A linear analysis of normal mode instability of the interface in an inclined closed tube is carried out using full Navier-Stokes equation using Chebyshev-tau method. It has been observed that Reynolds num...

Initial boundary value problems for the three-dimensional Kuramoto-Sivashinsky equation posed on unbounded 3D grooves (that may serve as mathematical models wildfires) were considered. The existence and uniqueness of global strong solutions well their exponential decay have been established.

Abstract It is shown that an oblique projection-based feedback control able to stabilize the state of Kuramoto–Sivashinsky equation, evolving in rectangular domains, a given time-dependent trajectory. The actuators consist finite number indicator functions supported small subdomains. Simulations are presented, one-dimensional case under periodic boundary conditions and two-dimensional Neumann c...

The universal field equations introduced by the author and his collaborators, which admit infinitely many inequivalent Lagrangian formulations are shown to arise as consistency conditions for the existence of non-trivial solutions to the quasi-linear equations, called equations of hydrodynamic type by Novikov , Dubrovin and others. The solutions in closed form are only implicit. A method due to...

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.