LEADER 04338nam 22006615 450 001 9911031568803321 005 20251001130713.0 010 $a3-031-96704-6 024 7 $a10.1007/978-3-031-96704-7 035 $a(CKB)41520824100041 035 $a(MiAaPQ)EBC32323690 035 $a(Au-PeEL)EBL32323690 035 $a(DE-He213)978-3-031-96704-7 035 $a(EXLCZ)9941520824100041 100 $a20251001d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOptimal Stability Theory and Approximate Solutions of Fractional Systems $eNew Results on the Analysis of Fractional Equations: Theoretical Insights and Numerical Approximations /$fby Zahra Eidinejad, Reza Saadati, Tofigh Allahviranloo, Chenkuan Li, Javad Vahidi 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (598 pages) 225 1 $aStudies in Systems, Decision and Control,$x2198-4190 ;$v606 311 08$a3-031-96703-8 327 $aBasic concepts Review -- Analysis of a new stability -- Analysis of a new stability on matrix valued fuzzy spaces -- Picard method -- Cellular neural networks, pseudo almost automorphic solution -- Z Numbers -- Analysis of numerical methods. 330 $aThis comprehensive book is designed for undergraduate, master's, and doctoral students in mathematics, as well as scholars interested in a deep understanding of fractional problems. The book covers a wide range of topics, including the existence and uniqueness of solutions, stability, optimal controllers, special functions, classical and fuzzy normed spaces, matrix functions, fuzzy matrix normed spaces, fixed-point theory, quality and certainty, and various numerical methods. The primary objective of this book is to analyze the existence and uniqueness of solutions for functional equations, analyze stability, and achieve the best possible results with minimal error. With a clear and direct approach, it presents advanced concepts in an accessible and comprehensible manner, enabling students to apply their knowledge to solving various problems. To prevent instability in fractional systems, methods based on fixed-point theory with the best approximation have been utilized. The stability analysis of fractional equations is conducted by considering classical and fuzzy normed spaces and employing special functions as optimal controllers. In fuzzy systems, the Z-number theory has been used to enhance results and improve quality. This theory enables the assessment of approximation accuracy and quality, providing the best possible approximation. The numerical analysis of fractional systems plays a crucial role in accurately modeling physical phenomena, simulations, and predicting complex systems. By presenting numerical results from fractional systems, which are essential in solving real-world problems and optimizing computational algorithms, this book serves as a valuable resource for both researchers and students. 410 0$aStudies in Systems, Decision and Control,$x2198-4190 ;$v606 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aDynamics 606 $aNonlinear theories 606 $aComputational intelligence 606 $aMathematical and Computational Engineering Applications 606 $aApplied Dynamical Systems 606 $aComputational Intelligence 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aDynamics. 615 0$aNonlinear theories. 615 0$aComputational intelligence. 615 14$aMathematical and Computational Engineering Applications. 615 24$aApplied Dynamical Systems. 615 24$aComputational Intelligence. 676 $a620 700 $aEidinejad$b Zahra$01850291 701 $aSaadati$b Reza$0768254 701 $aAllahviranloo$b Tofigh$01077219 701 $aLi$b Chenkuan$01737954 701 $aVahidi$b Javad$01850292 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911031568803321 996 $aOptimal Stability Theory and Approximate Solutions of Fractional Systems$94443293 997 $aUNINA