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020 _a9783031555640
_9978-3-031-55564-0
024 7 _a10.1007/978-3-031-55564-0
_2doi
050 4 _aQ342
072 7 _aUYQ
_2bicssc
072 7 _aCOM004000
_2bisacsh
072 7 _aUYQ
_2thema
100 1 _aRezaei Aderyani, Safoura.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_976000
245 1 0 _aTowards Ulam Type Multi Stability Analysis
_h[electronic resource] :
_bA Novel Approach for Fuzzy Dynamical Systems /
_cby Safoura Rezaei Aderyani, Reza Saadati, Chenkuan Li, Tofigh Allahviranloo.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIX, 571 p. 29 illus., 27 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aStudies in Systems, Decision and Control,
_x2198-4190 ;
_v523
505 0 _aIntroduction -- The Hypergeometric, Supertrigonometric, And Superhyperbolic Functions.-The Wright, Supertrigonometric And Superhyperbolic Functions -- The Mittag-Leffler, Supertrigonometric, And Superhyperbolic Functions -- The Wiman, Supertrigonometric, And Superhyperbolic Functions -- The Prabhakar, Supertrigonometric, And Superhyperbolic Functions -- The Sonine, Supertrigonometric And Superhyperbolic Functions -- Other Special Functions, Supertrigonometric And Superhyperbolic Functions -- Preliminaries -- Multi Stability Of The Jensen Type Random Operator Equations In C*-Algebras -- Super Multi Stability Of Additive Functional Inequalities In Banach Algebras -- Multi Stability Of Tri-Additive Functional Inequalities In Unital C*-Algebras -- Multi Stability Of Fractional-Order Systems I -- Multi Stability Of Fractional-Order System II -- Fuzzy Topological Spaces -- Multi Stability Of Pseudo Stochastic Tri{Additive Fuzzy Operator Inequalities In MVFC-\Diamond-Algebras -- Multi Stability Of Additive-Additive Fuzzy Functional Inequalities In MVFC-\Diamond-Ternary Algebras -- Multi Stability Of Pseudo Stochastic Additive Fuzzy Operator Inequalities In MVFB-Algebras -- Multi Stability Of Fractional-Order Volterra Equations In MVFB-Spaces -- Multi Stability Of Fractional-Order System I In MVFB-Spaces -- Multi Stability Of Fractional-Order System II In MVFB-Spaces -- The Matrix Mittag-Leffler Function And Nonlinear Fractional Integro-Differential Equations.
520 _aThe 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.
650 0 _aComputational intelligence.
_964052
650 0 _aDynamics.
_965524
650 0 _aNonlinear theories.
_965525
650 0 _aEngineering mathematics.
_964145
650 1 4 _aComputational Intelligence.
_964052
650 2 4 _aApplied Dynamical Systems.
_965530
650 2 4 _aEngineering Mathematics.
_964145
700 1 _aSaadati, Reza.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_976001
700 1 _aLi, Chenkuan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_976002
700 1 _aAllahviranloo, Tofigh.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_968757
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031555633
776 0 8 _iPrinted edition:
_z9783031555657
776 0 8 _iPrinted edition:
_z9783031555664
830 0 _aStudies in Systems, Decision and Control,
_x2198-4190 ;
_v523
856 4 0 _uhttps://doi.org/10.1007/978-3-031-55564-0
912 _aZDB-2-INR
912 _aZDB-2-SXIT
999 _c59491
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