By Snehashish Chakraverty, Smita Tapaswini, Diptiranjan Behera
Presents a scientific remedy of fuzzy fractional differential equations in addition to newly built computational the right way to version doubtful actual problems
Complete with finished effects and strategies, Fuzzy Arbitrary Order approach: Fuzzy Fractional Differential Equations and purposes details newly built equipment of fuzzy computational techniquesneeded to version clear up uncertainty. Fuzzy differential equations are solved through numerous analytical andnumerical methodologies, and this ebook provides their value for challenge fixing, prototypeengineering layout, and structures trying out in doubtful environments.
In contemporary years, modeling of differential equations for arbitrary and fractional order platforms has been expanding in its applicability, and as such, the authors characteristic examples from numerous disciplines to demonstrate the practicality and value of the equipment inside of physics, utilized arithmetic, engineering, and chemistry, to call a number of. the basics of fractional differential equations and the fundamental preliminaries of fuzzy fractional differential equations are first brought, through numerical strategies, comparisons of varied tools, and simulated effects. furthermore, fuzzy usual, partial, linear, and nonlinear fractional differential equations are addressed to resolve uncertainty in actual platforms. moreover, this e-book features:
- Basic preliminaries of fuzzy set thought, an creation of fuzzy arbitrary order differential equations, and numerous analytical and numerical systems for fixing linked problems
- Coverage on numerous fuzzy fractional differential equations together with structural, diffusion, and chemical difficulties in addition to warmth equations and biomathematical applications
- Discussions on tips to version actual difficulties by way of nonprobabilistic equipment and offers systematic insurance of fuzzy fractional differential equations and its applications
- Uncertainties in structures and tactics with a fuzzy concept
Fuzzy Arbitrary Order approach: Fuzzy Fractional Differential Equations and purposes is a fantastic source for practitioners, researchers, and academicians in utilized arithmetic, physics, biology, engineering, laptop technology, and chemistry who have to version doubtful actual phenomena and difficulties. The booklet is acceptable for graduate-level classes on fractional differential equations for college kids majoring in utilized arithmetic, engineering, physics, and desktop science.
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Additional resources for Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications
London, New York: Higher Education Press, Springer Heidelberg Dordrecht; 2011. Podlubny I. Fractional Differential Equations. New York, NY: Academic Press; 1999. Prakash P, Nieto JJ, Senthilvelavan S, Sudha Priya G. Fuzzy fractional initial value problem. J Intell Fuzzy Syst 2015,28:2691–2704. Ross TJ. Fuzzy Logic with Engineering Applications. New York: John Wiley & Sons; 2004. Saadatmandi A, Dehghan M. A new operational matrix for solving fractional order differential equations. Comput Math Appl 2010;59:1326–1336.
In this regard, first, we will briefly discuss the concept of n-term fuzzy fractional linear ordinary differential equations. In general, three cases may arise according to sign of the coefficients in the FFDEs. Finally, this chapter includes three analytical methods by considering three cases to solve n-term linear FFDEs as follows. Method 1: Fuzzy-Center-Based Method (FCM) (Tapaswini and Chakraverty, 2014a). Method 2: Method Based on Addition and Subtraction of Fuzzy Numbers (ASFM). Method 3: Double-Parametric-Based Method (DPM) (Tapaswini and Chakraverty, 2013, 2014a).
He JH. Variational iteration method for autonomous ordinary differential system. Appl Math Comput 2000b;114:115–123. 40 FUZZY ARBITRARY ORDER SYSTEM Himoun N, Abbaoui K, Cherruault Y. New results of convergence of Adomian’s method. Kybernetes 1999;28:423–429. Kazem S. Exact solution of some linear fractional differential equations by Laplace transform. Int J Nonlinear Sci 2013;16:3–11. Tapaswini S, Chakraverty S. Numerical solution of n-th order fuzzy linear differential equations by homotopy perturbation method.
Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications by Snehashish Chakraverty, Smita Tapaswini, Diptiranjan Behera
Categories: Differential Equations