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Time-fractional order biological systems with uncertain parameters /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Time-fractional order biological systems with uncertain parameters // Snehashish Chakraverty, Rajarama Mohan Jena, and Subrat Kumar Jena.
Author:	Chakraverty, Snehashish,
other author:	Jena, Rajarama Mohan,
Description:	1 PDF (xv, 144 pages) :illustrations (some color). :
Notes:	Part of: Synthesis digital library of engineering and computer science.
Subject:	Systems biology - Mathematical models. -
Online resource:	https://doi.org/10.2200/S00976ED1V01Y201912MAS031
Online resource:	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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100 1 $a Chakraverty, Snehashish, $e editor. $3 1057422
245 1 0 $a Time-fractional order biological systems with uncertain parameters / $c Snehashish Chakraverty, Rajarama Mohan Jena, and Subrat Kumar Jena.
264 1 $a [San Rafael, California] : $b Morgan & Claypool, $c [2020]
300 $a 1 PDF (xv, 144 pages) : $b illustrations (some color).
336 $a text $2 rdacontent
337 $a electronic $2 isbdmedia
338 $a online resource $2 rdacarrier
490 1 $a Synthesis lectures on mathematics and statistics, $x 1938-1751 ; $v #31
500 $a Part of: Synthesis digital library of engineering and computer science.
504 $a Includes bibliographical references.
505 0 $a 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
505 8 $a 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
505 8 $a 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
505 8 $a 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
505 8 $a 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 8 $a 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
505 8 $a 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
505 8 $a 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.
506 $a Abstract freely available; full-text restricted to subscribers or individual document purchasers.
510 0 $a Compendex
510 0 $a INSPEC
510 0 $a Google scholar
510 0 $a Google book search
520 $a 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.
530 $a Also available in print.
538 $a Mode of access: World Wide Web.
538 $a System requirements: Adobe Acrobat Reader.
588 $a Title from PDF title page (viewed on April 6, 2020).
650 0 $a Systems biology $x Mathematical models. $3 1000176
650 0 $a Biological systems $x Mathematical models. $3 583117
650 0 $a Fractional calculus $v Congresses. $3 1062477
650 0 $a Fuzzy sets. $3 559335
650 0 $a Fractional differential equations. $3 1132517
653 $a fractional calculus
653 $a fuzzy set theory
653 $a time-fractional differential equations
653 $a mathematical models
655 0 $a Electronic books. $2 local $3 554714
700 1 $a Jena, Rajarama Mohan, $e author. $3 1253163
700 1 $a Jena, Subrat Kumar, $e author. $3 1253164
776 0 8 $i Print version: $z 9781681737515 $z 9781681737492
830 0 $a Synthesis digital library of engineering and computer science. $3 598254
830 0 $a Synthesis lectures on mathematics and statistics ; $v #26. $3 1253098
856 4 0 $3 Abstract with links to full text $u https://doi.org/10.2200/S00976ED1V01Y201912MAS031
856 4 2 $3 Abstract with links to resource $u https://ieeexplore.ieee.org/servlet/opac?bknumber=9046352