In this paper, we will study a concepts of sectional intuitionistic fuzzy continuous and prove the schauder fixed point theorem in intuitionistic fuzzy metric space as a generalization of fuzzy metric space and prove a nother version of schauder fixed point theorem in intuitionistic fuzzy metric space as a generalization to the other types of fixed point theorems in intuitionistic fuzzy metric space considered by other researchers, as well as, to the usual intuitionistic fuzzy metric space.

            This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2  and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.

   This paper aims to prove an existence theorem for Voltera-type equation in a generalized G- metric space, called the -metric space, where the fixed-point theorem in - metric space is discussed and its application.  First, a new contraction of Hardy-Rogess type is presented and also then fixed point theorem is established for these contractions in the setup of -metric spaces. As application, an existence result for Voltera integral equation is obtained.  

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

   In this paper we prove a theorem about the existence and uniqueness common fixed point for two uncommenting self-mappings which defined on orbitally complete G-metric space. Where we use a general contraction condition.
 

     This research aims to utilize a complementarity of field excavations and laboratory works with spatial analyses techniques for a highly accurate modeling of soil geotechniques properties (i.e. having lower root mean square error value for the spatial interpolation). This was conducted, for a specified area of interest, firstly by adopting spatially sufficient and  well distributed samples (cores). Then, in the second step, a simulation is performed for the variations in properties when soil is contaminated with commonly used industrial material, which is white oil in our case. Cohesive (disturbed and undisturbed) soil samples were obtained from three various locations inside Baghdad University campus in AL-J

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.

Sufficient conditions for boundary controllability of nonlinear system in quasi-Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and some techniques of nonlinear functional analysis, such as, fixed point theorem and quasi-Banach contraction principle theorem. Moreover, we given an example which is provided to illustrate the theory.