Fuzzy arbitrary order system : fuzzy fractional differential equations and applications / / Snehashish Chakraverty, Smita Tapaswini, Diptiranjan Behera

• Record Nr.: UNINA9910135037603321
• Autore: Chakraverty Snehashish
• Pubbl/distr/stampa: Hoboken, New Jersey : , : Wiley, , 2016; ©2016
• ISBN: 1-119-00417-9; 1-119-00413-6; 1-119-00423-3
• Descrizione fisica: 1 online resource (275 p.)
• Disciplina: 515/.352
• Soggetti: Fractional differential equations; Fuzzy mathematics; Differential equations
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: Cover; Title Page; Copyright; Contents; Preface; Acknowledgments; Chapter 1 Preliminaries of Fuzzy Set Theory; Bibliography; Chapter 2 Basics of Fractional and Fuzzy Fractional Differential Equations; Bibliography; Chapter 3 Analytical Methods for Fuzzy Fractional Differential Equations (FFDES); 3.1 n-Term Linear Fuzzy Fractional Linear Differential Equations; 3.2 Proposed Methods; Bibliography; Chapter 4 Numerical Methods for Fuzzy Fractional Differential Equations; 4.1 Homotopy Perturbation Method (HPM); 4.2 Adomian Decomposition Method (ADM); 4.3 Variational Iteration Method (VIM); BibliographyChapter 5 Fuzzy Fractional Heat Equations; 5.1 Arbitrary-Order Heat Equation; 5.2 Solution of Fuzzy Arbitrary-Order Heat Equations by HPM; 5.3 Numerical Examples; 5.4 Numerical Results; Bibliography; Chapter 6 Fuzzy Fractional Biomathematical Applications; 6.1 Fuzzy Arbitrary-Order Predator-Prey Equations; 6.1.1 Particular Case; 6.2 Numerical Results of Fuzzy Arbitrary-Order Predator-Prey Equations; Bibliography; Chapter 7 Fuzzy Fractional Chemical Problems; ; 7.1 Arbitrary-Order Rossler's Systems; 7.2 HPM Solution of Uncertain Arbitrary-Order Rossler's System; 7.3 Particular Case; 7.3.1 Special Case7.4 Numerical Results; Bibliography; Chapter 8 Fuzzy Fractional Structural Problems; 8.1 Fuzzy Fractionally Damped Discrete System; 8.2 Uncertain Response Analysis; 8.2.1 Uncertain Step Function Response; 8.2.2 Uncertain Impulse Function Response; 8.3 Numerical Results; 8.3.1 Case Studies for Uncertain Step Function Response; 8.3.2 Case Studies for Uncertain Impulse Function Response; 8.4 Fuzzy Fractionally Damped Continuous System; 8.5 Uncertain Response Analysis; 8.5.1 Unit step Function Response; 8.5.2 Unit Impulse Function Response; 8.6 Numerical Results; 8.6.1 Case Studies for Fuzzy Unit Step Response8.6.2 Case Studies for Fuzzy Unit Impulse Response; Bibliography; Chapter 9 Fuzzy Fractional Diffusion Problems; 9.1 Fuzzy Fractional-Order Diffusion Equation; 9.1.1 Double-Parametric-Based Solution of Uncertain Fractional-Order Diffusion Equation; 9.1.2 Solution Bounds for Different External Forces; 9.2 Numerical Results of Fuzzy Fractional Diffusion Equation; Bibliography; Chapter 10 Uncertain Fractional Fornberg-Whitham Equations; 10.1 Parametric-Based Interval Fractional Fornberg-Whitham Equation; 10.2 Solution by VIM; 10.3 Solution Bounds for Different Interval Initial Conditions10.4 Numerical Results; Bibliography; Chapter 11 Fuzzy Fractional Vibration Equation of Large Membrane; 11.1 Double-Parametric-Based Solution of Uncertain Vibration Equation of Large Membrane; 11.2 Solutions of Fuzzy Vibration Equation of Large Membrane; 11.3 Case Studies (Solution Bounds for Particular Cases); 11.4 Numerical Results for Fuzzy Fractional Vibration Equation for Large Membrane; Bibliography; Chapter 12 Fuzzy Fractional Telegraph Equations; 12.1 Double-Parametric-Based Fuzzy Fractional Telegraph Equations; 12.2 Solutions of Fuzzy Telegraph Equations Using Homotopy Perturbation Method