Fractional Calculus (Mathematics Research Developments) by Roy Abi Zeid Daou, Xavier Moreau
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Overview: After presenting the first volume of this two-volume book, presenting a lot of mathematical and theoretical studies and research related to non-integer calculus, the second volume illustrates applications related to this domain. This volume is made up of 11 chapters. The first chapter presents the heuristic power of the non-integer differential operators in physics starting from the chaos to the emergence, the auto-organizations and the holistic rules. The second chapter shows the dynamics of the fractional order chaotic systems along with some applications.
The third chapter represents the pressure control of gas engines by non-integer order controllers by showing a novel trend in the application of the fractional calculus to automotive systems. Chapter 4 shows the way to model fractional order equations using state space modeling along with some applications. Another application related to this domain is the thermal diffusive interface. Chapter 5 shows the analysis of a semi-infinite diffuse plane medium along with the equations that model this medium, and some frequency and time domain responses. However, Chapter 6 treats this problem by controlling this plant using the well-known CRONE controller. Chapter 8 presents the adaptive second-order fractional sliding mode control with an application to a water tanks level system. Chapter 9 treats the mechanical aspect by showing the features of the fractional operators applied to this domain.
Genre: Non-Fiction > Educational
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