Fuzzy arbitrary order system : fuzzy fractional differential equations and applications /: fuzzy fractional differential equations and applications. (2015)

• Record Type: Book
• Further Information: Note: Snehashish Chakraverty, Smita Tapaswini, Diptiranjan Behera.
• Authors: Chakraverty, Snehashish; Tapaswini, Smita; Behera, Diptiranjan
• Contents: Preface Chapter 1: Preliminaries of Fuzzy Set Theory 1.1. Interval 1.2. Fuzzy Number 1.3. Triangular Fuzzy Number (TFN) 1.4. Trapezoidal Fuzzy Number (TrFN) 1.5. Gaussian Fuzzy Number (GFN) 1.6. Double Parametric Form of Fuzzy Number 1.7. Fuzzy Centre 1.8. Fuzzy Radius 1.9. Fuzzy Width 1.10. Fuzzy Arithmetic References Chapter 2: Basics of fractional and fuzzy fractional differential equations 2.1. Fuzzy Initial Value Problem (FIVP) 2.2. Fuzzy Boundary Value Problem (FBVP) 2.3. Riemann-Liouville Fractional integral 2.4. Fuzzy Riemann-Liouville Fractional integral 2.5. Caputo Derivative 2.6. Caputo-type fuzzy fractional derivatives 2.7. Fractional Initial Value Problem 2.8. Fuzzy Fractional Initial Value Problem References Chapter 3: Analytical Methods for Fuzzy Fractional Differential Equations (FFDEs) 3.1. n-term Linear Fuzzy Fractional Linear Differential Equations 3.2. Proposed Methods References 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) References Chapter 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 References Chapter 6: Fuzzy Fractional Bio-Mathematical Applications 6.1. Fuzzy Arbitrary Order Predator-Prey Equations 6.2. Numerical Results of Fuzzy Arbitrary Order Predator-Prey Equations References 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 7.4. Numerical Results References Chapter 8: Fuzzy Fractional Structural Problems 8.1. Fuzzy Fractionally Damped Discrete System 8.2. Uncertain Response Analysis 8.3. Numerical Results 8.4. Fuzzy Fractionally Damped Continuous System 8.5. Uncertain Response Analysis 8.6. Numerical Results References Chapter 9: Fuzzy Fractional Diffusion Problems 9.1. Fuzzy Fractional Order Diffusion Equation 9.2. Numerical Results of Fuzzy Fractional Diffusion Equation References Chapter 10: Uncertain Fractional Fornberg-Whitham Equations 10.1. Parametric based interval fractional Fornberg-Whitham equation 10.2. Solution by VIM using proposed methodology 10.3. Solution bounds for different interval initial conditions 10.4. Numerical results References 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 References 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 12.3. Solution Bounds for Particular Cases 12.4. Numerical Results References Chapter 13: Fuzzy Fokker-Planck equation with space and time fractional derivatives 13.1. Fuzzy fractional Fokker-Planck equation with space and time fractional derivatives 13.2. Double parametric based solution of uncertain fractional Fokker-Planck equation 13.3. Case studies using HPM and ADM. 13.4. Numerical Results References Chapter 14: Fuzzy fractional Bagley-Torvik equations 14.1. Various types of Fuzzy fractional Bagley-Torvik equations 14.2. Results and Discussions References Appendix Index
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 515.83; Fractional differential equations; Fuzzy mathematics
• Languages: English
• ISBNs: 9781119004172
• Related ISBNs: 9781119004134
• Notes: Note: Description based on CIP data; resource not viewed.
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