This opening lecture is intended to serve as a propaedeutic for the papers to be presented at this conference whose nonhomogeneous audience includes scientists, mathematicians, engineers and educators. This expository and developmental lecture, a case study of mathematical growth, surveys the origin and development of a mathematical idea from its birth in intellectual curiosity to applications....

Depth image enhancement techniques can help to improve quality and facilitate computer vision tasks. Traditional image-enhancement methods, which are typically based on integer-order calculus, cannot exploit the textural information of an image, their effect is limited. To solve this problem, fractional differentiation has been introduced as innovative image-processing tool. It enables flexible...

Integration, just as much differentiation, is a fundamental calculus tool that widely used in many scientific domains. Formalizing the mathematical concept of integration and associated results formal proof assistant helps providing highest confidence on correctness numerical programs involving use integration, directly or indirectly. By its capability to extend (Riemann) integral wide class ir...

the current study presents a new analytical method for buckling analysis of rectangular and annular beams made up of functionally graded materials with constant thickness and poisson’s ratio. the boundary conditions of the beam are assumed to be simply supported and clamped. the stability equations were obtained by using conservation of energy. the critical buckling load and first mode shape we...

the current study presents a new analytical method for buckling analysis of circular plates with constant thickness and poisson’s ratio, made of functionally graded material subjected to radial load. governing equations are based on energy method for thin plates. the boundary conditions of the plate are assumed to be simply supported and clamped. the stability equations were obtained by using c...

The worldwide energy revolution has accelerated the utilization of demand-side manageable systems such as wind turbines, photovoltaic panels, electric vehicles, and storage in order to deal with growing crisis greenhouse emissions. control system renewable units a high effect on their performance absolutely efficiency total power network. Classical controllers are based integer-order differenti...

Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional (FC) based on fractional-order thinking (FOT) has been shown to help us understand complex systems better, improve processing signals, enhance control systems, increase performance optimization, even extend enabling potential for creativity. In this article, authors discuss fractional dynami...

This paper aims at investigating the superiority of power allocation strategies, based on calculus of variations in a point-to-point two-way relay-assisted channel incorporating the amplify and forward strategy. Single and multilayer coding strategies for two cases of having and not having the channel state information (CSI) at the transmitters are studied, respectively. Using the notion of cal...