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This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions. Illustrating theoretical results via applications in special means of real numbers, it is an essential reference for applied mathematicians and engineers working with fractional calculus. ContentsIntroductionPreliminariesFractional integral identitiesHermite-Hadamard inequalities involving Riemann-Liouville fractional integralsHermite-Hadamard inequalities involving Hadamard fractional integrals

Fractional calculus. --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus

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This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. ContentsFractional Difference EquationsFractional Integral EquationsFractional Differential EquationsFractional Evolution Equations: ContinuedFractional Differential Inclusions

Fractional calculus. --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus

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Stability and Controls Analysis for Delay Systems is devoted to stability, controllability and iterative learning control (ILC) to delay systems, including first order system, oscillating systems, impulsive systems, fractional systems, difference systems and stochastic systems raised from physics, biology, population dynamics, ecology and economics, currently not presented in other books on conventional fields. Delayed exponential matrix function approach is widely used to derive the representation and stability of the solutions and the controllability. ILC design are also established, which can be regarded as a way to find the control function. The broad variety of achieved results with rigorous proofs and many numerical examples make this book unique.

Control theory. --- Time delay systems. --- Time delay control --- Time delay control systems --- Time delay controllers --- Time-delayed systems --- Feedback control systems --- Process control --- Dynamics --- Machine theory

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This book introduces iterative learning control (ILC) and its applications to the new equations such as fractional order equations, impulsive equations, delay equations, and multi-agent systems, which have not been presented in other books on conventional fields. ILC is an important branch of intelligent control, which is applicable to robotics, process control, and biological systems. The fractional version of ILC updating laws and formation control are presented in this book. ILC design for impulsive equations and inclusions are also established. The broad variety of achieved results with rigorous proofs and many numerical examples make this book unique. This book is useful for graduate students studying ILC involving fractional derivatives and impulsive conditions as well as for researchers working in pure and applied mathematics, physics, mechanics, engineering, biology, and related disciplines.

Mathematical analysis --- Mathematics --- Electrical engineering --- Applied physical engineering --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- analyse (wiskunde) --- mechatronica --- industriële robots --- automatisering --- economie --- informatica --- systeemtheorie --- wiskunde --- ingenieurswetenschappen --- robots --- automatische regeltechniek