Time-fractional order biological systems with uncertain parameters / Snehashish Chakraverty, Rajarama Mohan Jena, and Subrat Kumar Jena

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Chakraverty, Snehashish [VerfasserIn]

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Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Synthesis lectures on mathematics and statistics ; #31Verlag: [San Rafael, California] : Morgan & Claypool, [2020]Beschreibung: 1 Online-Ressource (xv, 144 pages) : illustrations (some color)ISBN:

1681737507
9781681737508

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Andere physische Formen: 1681737515 | 9781681737492 | 1681737493 | 9781681737515 | Erscheint auch als: 9781681737515 Druck-AusgabeDDC-Klassifikation:

570.113

LOC-Klassifikation:

QH324.2

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Zusammenfassung: 1. Preliminaries to fractional calculus -- 1.1. Introduction -- 1.2. Birth of fractional calculus -- 1.3. Popular definitions of fractional derivatives and integrals -- 1.4. ReferencesZusammenfassung: 2. Preliminaries of fuzzy set theory -- 2.1. Introduction -- 2.2. Interval -- 2.3. Interval arithmetic -- 2.4. Fuzzy set -- 2.5. [gamma]-cut -- 2.6. Fuzzy number -- 2.7. Double parametric form (DPF) of fuzzy number -- 2.8. Fuzzy fractional Reimann-Liouville integral -- 2.9. Fuzzy fractional Caputo derivative -- 2.10. Fractional initial value problem (FIVP) -- 2.11. Fuzzy fractional initial value problem (FFIVP) -- 2.12. Fractional boundary value problem (fbvp) -- 2.13. Fuzzy fractional boundary value problem (ffbvp) -- 2.14. ReferencesZusammenfassung: 3. Fuzzy fractional differential equations and method of solution -- 3.1. Introduction -- 3.2. Description of fractional reduced differential transform method -- 3.3. Numerical examples -- 3.4. ReferencesZusammenfassung: 4. Imprecisely defined time-fractional model of cancer chemotherapy effect -- 4.1. Introduction -- 4.2. Mathematical model -- 4.3. Mathematical model with fuzzy parameters -- 4.4. Results and discussion -- 4.5. ReferencesZusammenfassung: 5. Fuzzy time-fractional smoking epidemic model -- 5.1. Introduction -- 5.2. Mathematical model -- 5.3. Equilibrium point and stability -- 5.4. Mathematical model with fuzzy parameters -- 5.5. Numerical results and discussion -- 5.6. ReferencesZusammenfassung: 6. Time-fractional model of HIV-I infection of CD4+ T lymphocyte cells in uncertain environment -- 6.1. Introduction -- 6.2. Mathematical model with fuzzy initial conditions -- 6.3. Numerical results and discussion -- 6.4. ReferencesZusammenfassung: 7. Time-fractional model of hepatitis E virus with uncertain parameters -- 7.1. Introduction -- 7.2. Mathematical model -- 7.3. Mathematical model with fuzzy initial conditions -- 7.4. Numerical results and discussion -- 7.5. ReferencesZusammenfassung: 8. Fuzzy time-fractional SIRS-SI malaria disease model -- 8.1. Introduction -- 8.2. Mathematical model -- 8.3. Mathematical model with fuzzy initial conditions -- 8.4. Results and discussion -- 8.5. References.Zusammenfassung: The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, PI[lambda][mu] controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters. However, in real-life applications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge. In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globePPN: PPN: 175515870XPackage identifier: Produktsigel: BSZ-4-NLEBK-KAUB | ZDB-4-NLEBK

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