The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

أن هذه الدراسة هي دراسة نظرية اهتمت بتقديم مدخل معاصر لمنظمات الأعمال، يمكن أن يعتمد علية من أجل تحقيق الريادة و البقاء. وذلك من خلال اعتماد مدخل الهدم الخلاق و تقديم أنموذج قادر على التفاعل مع البيئة بكل ما تقدمه من فرص وتحديات.

وتم تقسيم هذه الدراسة إلى ثلاثة مباحث،تناول المبحث الأول منهجية الدراسة. وبينما تناول المبحث الثاني توضيح مفهوم الهدم الخلاق والعناصر المكونة لهذا المدخل وأخيراً

In this paper, a procedure to establish the different performance measures in terms of crisp value is proposed for two classes of arrivals and multiple channel queueing models, where both arrival and service rate are fuzzy numbers. The main idea is to convert the arrival rates and service rates under fuzzy queues into crisp queues by using graded mean integration approach, which can be represented as median rule number. Hence, we apply the crisp values obtained to establish the performance measure of conventional multiple queueing models. This procedure has shown its effectiveness when incorporated with many types of membership functions in solving queuing problems. Two numerical illustrations are presented to determine the validity of the

We introduce and discuss recent type of fibrewise topological spaces, namely fibrewise soft bitopological spaces. Also, we introduce the concepts of fibrewise closed soft bitopological spaces, fibrewise open soft bitopological spaces, fibrewise locally sliceable soft bitopological spaces and fibrewise locally sectionable soft bitopological spaces. Furthermore, we state and prove several propositions concerning these concepts.

Abstract. One of the fibrewise micro-topological space is one in which the topology is decided through a group of fibre bundles, in comparison to the usual case in normal, fibrewise topological space. The micro-topological spaces draw power from their ability to be used in descriptions of a wide range of mathematical objects. These can be used to describe the topology of a manifold or even the topology of a group. Apart from easy manipulation, the fibrewise micro-topological spaces yield various mathematical applications, but the one being mentioned here is the possibility for geometric investigation of space or group structure. In this essay, we shall explain what fibrewise micro-topological spaces are, indicate why they are useful in math

We define and study new ideas of fibrewise topological space on D namely fibrewise multi-topological space on D. We also submit the relevance of fibrewise closed and open topological space on D. Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space on D. Furthermore, we propose and prove a number of statements about these ideas.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near topological spaces over B. Also, we introduce the concepts of fibrewise near closed and near open topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.