In this paper, we derive numerical and closed form solutions of fractional order Fibonacci difference equation and Generalized finite series of fractional Fibonacci summation formula using forward Fibonacci delta operator with several parameters and its inverse on real valued functions. Suitable examples are provided to illustrate our findings.

Mixed convection magnetohydrodynamic flow due to vertical permeable shrinking surface with radiation, heat generation and dissipation effects have been analyzed. The boundary conditions take into account of the slip due to velocity and jump in temperature. To convert the highly nonlinear partial differential equations into nonlinear ordinary differential equations, the appropriate similarity transformations are employed. Fourth order Runge Kutta based shooting method is used to solve the reduced coupled ordinary differential equations and Nachtsheim Swigert shooting iteration scheme is applied to satisfy the asymptotic boundary conditions. To expose the trend of the dimensionless velocity and dimensionless temperature, numerical results are presented for various pertinent parameters involved in the investigation. In addition to that the skin friction coefficient and dimensionless rate of heat transfer are portrayed through tables. The influence of velocity slip parameter is to accelerate the dimensionless velocity and decrease the dimensionless temperature. Enhancement in thermal slip parameter leads to reduction in fluid temperature.

The concept of generalized closed sets plays a significant role in General Topology and they are the research topics of many Topologists worldwide. In 1970, Levine [3] introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. P.Sundaram [5] studied the properties of weakly closed sets and weak continuous functions. Recently Lellis Thivagar et al. [2] initiated the concept of N-topological space and defined its related open sets. Also, they [2] studied the properties of some weak form of open sets in N-topological space. In this paper, some new classes of generalized closed sets in N-topological space have been introduced. Using these sets, the class of generalized closed sets N?G?C(X) lies between the class of closed sets N?C(X) and the class of generalized closed sets N?GC(X) has been established. Moreover as an application to it, I establish some new separation axioms.

In this article, the author explains about, how to draw complete fuzzy graph with M coloring and also explain how use chromatic number concept.The chromatic number represent the traffic signal in crowded city. By using coloring concept for signal lights and use fuzzy number for distance of the traveller. And also discussed how to reduce waiting time and traffic jam to reach the destination.

This paper aims to introduce the local function of a set with respect to an operation $\gamma$ on $\om$ and a new class of set known as ${\rama}I$-open set. It's basic properties have been derived along with suitable examples. However, some new class of spaces such as $\ramai$-regular space, $\ramai$-Hausdorff space and $\ramai$-normal space have been investigated and a few theorems based on these spaces have been derived.

Technology increases at break-neck speed. Year after year, computer-based technological advances have shaped and revolutionized how we interact with the world, a world that was inconceivable a few short decades ago. For many people, trying to find where they fit into this high-tech world can be a challenge. Attempting to match their interests and aptitudes to a future career can be confusing. Many careers in technical fields require the use of math. The quickly growing field of cyber security is no exception. In this paper we explain the concept of cybersecurity in a mathematical perspective.

The achromatic number for a graph G = (V, E) is the largest integer m such that there is a partition of V into disjoint independent sets (V1,�,Vm) satisfying the condition that for each pair of distinct sets V_i,V_j,V_i?V_j is not an independent set in G. In this paper, we present O(1) approximation algorithm to determine the achromatic number of web graph.

A numerical investigation has been carried out to analyze the effects of variable viscosity and thermal conductivity using fractional derivatives of Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) for MHD flow past an impulsively started vertical plate with ramped temperature and concentration.. Since a fluid�s viscosity and thermal conductivity depend on temperature, these characteristics are considered to be a variable. Using appropriate similarity transformations, the leading partial differential equations together with the boundary conditions are reduces dimensionless so that physical parameters occur in the equations and interpretations can be performed appropriately on these parameters. Using ordinary finite difference method, the equations thus obtained are discritized and we solved the discritized equations numerically using a method based on the iteration scheme of the Gauss-Seidel. Numerical techniques are used to find the values from AB and CF formulae for fractional derivatives with respect to time. The consequences of various parameters involved in the problem viz., viscosity parameter, thermal conductivity parameter, magnetic field parameter, Eckert number, Reynolds number, Schmidt number radiation parameter, chemical reaction parameter etc. on velocity, temperature, and concentration distribution at the plate have been shown graphically. The coefficient of skin-friction, heat transfer rate, and Sherwood number are also obtained and offered in tabular form. It has been found that each parameter�s effects are prominent enough. A comparison of the AB and CF methods in tabular form has also been presented. It is noticed that both approaches have been well agreed upon.