In this paper, we present an approximate method for solving integro-differential equations of multi-fractional order by using the variational iteration method.
First, we derive the variational iteration formula related to the considered problem, then prove its convergence to the exact solution. Also we give some illustrative examples of linear and nonlinear equations.

      This paper is concerned with the controllability of a nonlinear impulsive fractional integro-differential nonlocal control system with state-dependent delay in a Banach space. At first, we introduce a mild solution for the control system by using fractional calculus and probability density function. Under sufficient conditions, the results are obtained by means of semigroup theory and the Krasnoselskii fixed point theorem. Finally, an example is given to illustrate the main results.

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

      The aim of this article is to present the exact analytical solution for models as system of (2+1) dimensional PDEs by using a reliable manner based on combined LA-transform with decomposition technique and the results have shown a high-precision, smooth and speed convergence to the exact solution compared with other classic methods. The suggested approach does not need any discretization of the domain or presents assumptions or neglect for a small parameter in the problem and does not need to convert the nonlinear terms into linear ones. The convergence of series solution has been shown with two illustrated examples such (2+1)D- Burger's system and (2+1)D- Boiti-Leon-Pempinelli (BLP) system.

In this paper, we model the spread of coronavirus (COVID -19) by introducing stochasticity into the deterministic differential equation susceptible  -infected-recovered (SIR model). The stochastic SIR dynamics are expressed using Itô's formula. We then prove that this stochastic SIR has a unique global positive solution I(t).The main aim of this article is to study the spread of coronavirus COVID-19 in Iraq from 13/8/2020 to 13/9/2020. Our results provide a new insight into this issue, showing that the introduction of stochastic noise into the  deterministic model for the spread of COVID-19 can cause the disease to die out, in scenarios where deterministic models predict disease persistence. These results were also clearly ill