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Time-fractional order biological sys...
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Jena, Subrat Kumar,
Time-fractional order biological systems with uncertain parameters /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Time-fractional order biological systems with uncertain parameters // Snehashish Chakraverty, Rajarama Mohan Jena, and Subrat Kumar Jena.
作者:
Chakraverty, Snehashish,
其他作者:
Jena, Rajarama Mohan,
面頁冊數:
1 PDF (xv, 144 pages) :illustrations (some color). :
附註:
Part of: Synthesis digital library of engineering and computer science.
標題:
Systems biology - Mathematical models. -
電子資源:
https://doi.org/10.2200/S00976ED1V01Y201912MAS031
電子資源:
https://ieeexplore.ieee.org/servlet/opac?bknumber=9046352
ISBN:
9781681737508
Time-fractional order biological systems with uncertain parameters /
Chakraverty, Snehashish,
Time-fractional order biological systems with uncertain parameters /
Snehashish Chakraverty, Rajarama Mohan Jena, and Subrat Kumar Jena. - 1 PDF (xv, 144 pages) :illustrations (some color). - Synthesis lectures on mathematics and statistics,#311938-1751 ;. - Synthesis digital library of engineering and computer science..
Part of: Synthesis digital library of engineering and computer science.
Includes bibliographical references.
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. References
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
Compendex
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 globe.
Mode of access: World Wide Web.
ISBN: 9781681737508
Standard No.: 10.2200/S00976ED1V01Y201912MAS031doiSubjects--Topical Terms:
1000176
Systems biology
--Mathematical models.Subjects--Index Terms:
fractional calculusIndex Terms--Genre/Form:
554714
Electronic books.
LC Class. No.: QH324.2 / .C538 2020eb
Dewey Class. No.: 570.113
Time-fractional order biological systems with uncertain parameters /
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Time-fractional order biological systems with uncertain parameters /
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Snehashish Chakraverty, Rajarama Mohan Jena, and Subrat Kumar Jena.
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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. References
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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. References
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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. References
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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. References
505
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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. References
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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. References
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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.
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