{"product_id":"fuzzy-arbitrary-order-system-9781119004110","title":"Fuzzy Arbitrary Order System","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePresents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eComplete with comprehensive results and solutions, \u003ci\u003eFuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications \u003c\/i\u003edetails newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty. Fuzzy differential equations are solved via various analytical andnumerical methodologies, and this book presents their importance for problem solving, prototypeengineering design, and systems testing in uncertain environments.\u003c\/p\u003e \u003cp\u003eIn recent years, modeling of differential equations for arbitrary and fractional order systems has been increasing in its applicability, and as such, the authors feature examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to name\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePREFACE ix\u003c\/p\u003e \u003cp\u003eACKNOWLEDGMENTS xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Preliminaries of Fuzzy Set Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBibliography 7\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Basics of Fractional and Fuzzy Fractional Differential Equations 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBibliography 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Analytical Methods for Fuzzy Fractional Differential Equations (FFDES) 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 n-Term Linear Fuzzy Fractional Linear Differential Equations 16\u003c\/p\u003e \u003cp\u003e3.2 Proposed Methods 18\u003c\/p\u003e \u003cp\u003eBibliography 28\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Numerical Methods for Fuzzy Fractional Differential Equations 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Homotopy Perturbation Method (HPM) 31\u003c\/p\u003e \u003cp\u003e4.2 Adomian Decomposition Method (ADM) 35\u003c\/p\u003e \u003cp\u003e4.3 Variational Iteration Method (VIM) 37\u003c\/p\u003e \u003cp\u003eBibliography 39\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Fuzzy Fractional Heat Equations 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Arbitrary-Order Heat Equation 41\u003c\/p\u003e \u003cp\u003e5.2 Solution of Fuzzy Arbitrary-Order Heat Equations by HPM 41\u003c\/p\u003e \u003cp\u003e5.3 Numerical Examples 43\u003c\/p\u003e \u003cp\u003e5.4 Numerical Results 45\u003c\/p\u003e \u003cp\u003eBibliography 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Fuzzy Fractional Biomathematical Applications 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Fuzzy Arbitrary-Order Predator–Prey Equations 49\u003c\/p\u003e \u003cp\u003e6.1.1 Particular Case 51\u003c\/p\u003e \u003cp\u003e6.2 Numerical Results of Fuzzy Arbitrary-Order Predator–Prey Equations 54\u003c\/p\u003e \u003cp\u003eBibliography 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Fuzzy Fractional Chemical Problems 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Arbitrary-Order Rossler’s Systems 67\u003c\/p\u003e \u003cp\u003e7.2 HPM Solution of Uncertain Arbitrary-Order Rossler’s System 68\u003c\/p\u003e \u003cp\u003e7.3 Particular Case 71\u003c\/p\u003e \u003cp\u003e7.3.1 Special Case 73\u003c\/p\u003e \u003cp\u003e7.4 Numerical Results 78\u003c\/p\u003e \u003cp\u003eBibliography 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Fuzzy Fractional Structural Problems 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Fuzzy Fractionally Damped Discrete System 88\u003c\/p\u003e \u003cp\u003e8.2 Uncertain Response Analysis 90\u003c\/p\u003e \u003cp\u003e8.2.1 Uncertain Step Function Response 90\u003c\/p\u003e \u003cp\u003e8.2.2 Uncertain Impulse Function Response 93\u003c\/p\u003e \u003cp\u003e8.3 Numerical Results 96\u003c\/p\u003e \u003cp\u003e8.3.1 Case Studies for Uncertain Step Function Response 97\u003c\/p\u003e \u003cp\u003e8.3.2 Case Studies for Uncertain Impulse Function Response 100\u003c\/p\u003e \u003cp\u003e8.4 Fuzzy Fractionally Damped Continuous System 101\u003c\/p\u003e \u003cp\u003e8.5 Uncertain Response Analysis 110\u003c\/p\u003e \u003cp\u003e8.5.1 Unit step Function Response 110\u003c\/p\u003e \u003cp\u003e8.5.2 Unit Impulse Function Response 111\u003c\/p\u003e \u003cp\u003e8.6 Numerical Results 112\u003c\/p\u003e \u003cp\u003e8.6.1 Case Studies for Fuzzy Unit Step Response 114\u003c\/p\u003e \u003cp\u003e8.6.2 Case Studies for Fuzzy Unit Impulse Response 115\u003c\/p\u003e \u003cp\u003eBibliography 118\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Fuzzy Fractional Diffusion Problems 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Fuzzy Fractional-Order Diffusion Equation 121\u003c\/p\u003e \u003cp\u003e9.1.1 Double-Parametric-Based Solution of Uncertain\u003c\/p\u003e \u003cp\u003eFractional-Order Diffusion Equation 123\u003c\/p\u003e \u003cp\u003e9.1.2 Solution Bounds for Different External Forces 125\u003c\/p\u003e \u003cp\u003e9.2 Numerical Results of Fuzzy Fractional Diffusion Equation 130\u003c\/p\u003e \u003cp\u003eBibliography 139\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Uncertain Fractional Fornberg–Whitham Equations 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Parametric-Based Interval Fractional Fornberg–Whitham\u003c\/p\u003e \u003cp\u003eEquation 141\u003c\/p\u003e \u003cp\u003e10.2 Solution by VIM 143\u003c\/p\u003e \u003cp\u003e10.3 Solution Bounds for Different Interval Initial Conditions 145\u003c\/p\u003e \u003cp\u003e10.4 Numerical Results 148\u003c\/p\u003e \u003cp\u003eBibliography 152\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Fuzzy Fractional Vibration Equation of Large Membrane 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Double-Parametric-Based Solution of Uncertain Vibration Equation of Large Membrane 156\u003c\/p\u003e \u003cp\u003e11.2 Solutions of Fuzzy Vibration Equation of Large Membrane 158\u003c\/p\u003e \u003cp\u003e11.3 Case Studies (Solution Bounds for Particular Cases) 160\u003c\/p\u003e \u003cp\u003e11.4 Numerical Results for Fuzzy Fractional Vibration Equation for Large Membrane 172\u003c\/p\u003e \u003cp\u003eBibliography 188\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Fuzzy Fractional Telegraph Equations 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Double-Parametric-Based Fuzzy Fractional Telegraph Equations 191\u003c\/p\u003e \u003cp\u003e12.2 Solutions of Fuzzy Telegraph Equations Using Homotopy Perturbation Method 194\u003c\/p\u003e \u003cp\u003e12.3 Solution Bounds for Particular Cases 195\u003c\/p\u003e \u003cp\u003e12.4 Numerical Results for Fuzzy Fractional Telegraph Equations 199\u003c\/p\u003e \u003cp\u003eBibliography 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Fuzzy Fokker–Planck Equation with Space and Time Fractional Derivatives 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Fuzzy Fractional Fokker–Planck Equation with Space and Time Fractional Derivatives 207\u003c\/p\u003e \u003cp\u003e13.2 Double-Parametric-Based Solution of Uncertain Fractional Fokker–Planck Equation 209\u003c\/p\u003e \u003cp\u003e13.2.1 Solution by HPM 209\u003c\/p\u003e \u003cp\u003e13.2.2 Solution By ADM 210\u003c\/p\u003e \u003cp\u003e13.3 Case Studies Using HPM and ADM 211\u003c\/p\u003e \u003cp\u003e13.3.1 Using HPM 211\u003c\/p\u003e \u003cp\u003e13.3.2 Using ADM 215\u003c\/p\u003e \u003cp\u003e13.4 Numerical Results of Fuzzy Fractional Fokker–Planck Equation 218\u003c\/p\u003e \u003cp\u003eBibliography 220\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Fuzzy Fractional Bagley–Torvik Equations 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Various Types of Fuzzy Fractional Bagley–Torvik Equations 223\u003c\/p\u003e \u003cp\u003e14.2 Results and Discussions 231\u003c\/p\u003e \u003cp\u003eBibliography 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAPPENDIX A 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Fractionally Damped Spring–Mass System (Problem 1) 243\u003c\/p\u003e \u003cp\u003eA.1.1 Response Analysis 246\u003c\/p\u003e \u003cp\u003eA.1.2 Analytical Solution Using Fractional Green’s Function 247\u003c\/p\u003e \u003cp\u003eA.2 Fractionally Damped Beam (Problem 2) 248\u003c\/p\u003e \u003cp\u003eA.2.1 Response Analysis 250\u003c\/p\u003e \u003cp\u003eA.2.2 Numerical Results 251\u003c\/p\u003e \u003cp\u003eBibliography 255\u003c\/p\u003e \u003cp\u003eINDEX 257\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406965842263,"sku":"9781119004110","price":78.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119004110.jpg?v=1730497718","url":"https:\/\/bookcurl.com\/products\/fuzzy-arbitrary-order-system-9781119004110","provider":"Book Curl","version":"1.0","type":"link"}