The main target of this book is to present a new concept of Ulam-type stability, i.e., multi-stability, through the classical, well-known special functions and to obtain the best approximation error estimates by a dif...
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ISBN:
(数字)9783031555640
ISBN:
(纸本)9783031555633;9783031555664
The main target of this book is to present a new concept of Ulam-type stability, i.e., multi-stability, through the classical, well-known special functions and to obtain the best approximation error estimates by a different concept of perturbation stability including fuzzy approaches for uncertainty considerations. This stability allows us to obtain diverse approximations depending on various special functions that are initially chosen and to evaluate maximal stability and minimal error which enable us to obtain a unique optimal solution of functional equations, inequalities, and fractional equations. Stability analysis in the sense of the Ulam and its different kinds has received considerable attention from the researchers. However, how to effectively generalize the Ulam stability problems and to evaluate optimized controllability and stability are new issues. The multi-stability not only covers the previous concepts but also considers the optimization of the problem and provides a comprehensive discussion of optimizing the different types of the Ulam stabilities of mathematical models used in the natural sciences and engineering disciplines with fuzzy attitudes. Besides, this book also deals with nonlinear differential equations with various boundary conditions or initial value problems, based on the matrix Mittag-Leffler function, fixed point theory, as well as Babenko's approach to study uniqueness and existence of solutions. In general, the benefits for the readers can be concluded as follows:;1. Evaluates maximal stability with minimal error to get a unique optimal solution.;2. Discusses an optimal method of the alternative to study existence, uniqueness, and different types of Ulam stabilities under special consideration of the fuzzy approaches.;3. Delves into the new study of boundary value problems of fractional integro-differential equations with integral boundary conditions and variable coefficients.
Environmental protection and disaster risk topics are challenging fields, that scientific world is trying to address as much as it can. Earthquakes, floods, fires, droughts, blizzards, dust storms, natural releases of...
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ISBN:
(数字)9783030701901
ISBN:
(纸本)9783030701895;9783030701925
Environmental protection and disaster risk topics are challenging fields, that scientific world is trying to address as much as it can. Earthquakes, floods, fires, droughts, blizzards, dust storms, natural releases of toxic gases and liquids, diseases and other environmental variations affect hundreds of millions of people each year. Many disaster events are triggered by human activities. Dealing with these problems will require systems thinking and integrating multidisciplinary science. Actions in these directions are taken more and more in the recent years by political bodies, NGOs and scientific groups trying to find sustainable solutions for the future generations. Every point of view matter when it comes to our global home – The Planet Earth.
These works constitute advances in the aforementioned scientific fields and will be used by graduate as well as doctoral students along with established researchers to update themselves with the state of the art and r...
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ISBN:
(数字)9783031275401
ISBN:
(纸本)9783031275395;9783031275425
These works constitute advances in the aforementioned scientific fields and will be used by graduate as well as doctoral students along with established researchers to update themselves with the state of the art and recent advances in their respective fields. As the book includes several applicative studies with several multi-disciplinary contributions (deep learning, reinforcement learning, model-based/data-based control etc.), the book proves to be equally useful for the practitioners as well industrial professionals.
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