05647nam a22005415i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050000900172072001600181072002300197072001500220100009400235245019800329250001800527264006900545300006500614336002600679337002600705338003600731347002400767490006400791505148100855520194902336650003904285650002104324650003104345650003604376650003904412650003804451650003604489700008304525700008204608700009104690710003404781773002604815776003604841776003604877776003604913830006404949856004605013912001405059912001505073999001705088978-3-031-55564-0DE-He21320251030112018.0cr nn 008mamaa240429s2024    sz |    s    |||| 0|eng d  a97830315556409978-3-031-55564-07 a10.1007/978-3-031-55564-02doi 4aQ342 7aUYQ2bicssc 7aCOM0040002bisacsh 7aUYQ2thema1 aRezaei Aderyani, Safoura.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97600010aTowards Ulam Type Multi Stability Analysish[electronic resource] :bA Novel Approach for Fuzzy Dynamical Systems /cby Safoura Rezaei Aderyani, Reza Saadati, Chenkuan Li, Tofigh Allahviranloo.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIX, 571 p. 29 illus., 27 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aStudies in Systems, Decision and Control,x2198-4190 ;v5230 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.  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. 0aComputational intelligence.964052 0aDynamics.965524 0aNonlinear theories.965525 0aEngineering mathematics.96414514aComputational Intelligence.96405224aApplied Dynamical Systems.96553024aEngineering Mathematics.9641451 aSaadati, Reza.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9760011 aLi, Chenkuan.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9760021 aAllahviranloo, Tofigh.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9687572 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303155563308iPrinted edition:z978303155565708iPrinted edition:z9783031555664 0aStudies in Systems, Decision and Control,x2198-4190 ;v52340uhttps://doi.org/10.1007/978-3-031-55564-0  aZDB-2-INR  aZDB-2-SXIT  c59491d59491