Recent trends in fractional calculus and its applications /
This scholarly work focuses on the recent advancements in fractional calculus and its applications within complex systems. Edited by Praveen Agarwal and other prominent mathematicians, the book provides a comprehensive overview of fractional calculus, emphasizing its role in mathematical modeling an...
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| Формат: | Электронный ресурс eКнига |
| Язык: | английский |
| Опубликовано: |
[S.l.] :
Academic Press,
2024.
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| Серии: | Advanced studies in complex systems
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| Предметы: | |
| Online-ссылка: | ScienceDirect |
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| 245 | 0 | 0 | |a Recent trends in fractional calculus and its applications / |c edited by Praveen Agarwal [and more]. |
| 260 | |a [S.l.] : |b Academic Press, |c 2024. | ||
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| 490 | 0 | |a Advanced studies in complex systems | |
| 505 | 8 | |a 4.4.1 Variable-order Riemann-Liouville pseudo-operational matrix of fractional-order Fibonacci wavelets -- 4.4.1.1 Fractional-order piecewise Taylor functions -- 4.4.1.2 Transformation matrix of FFWs into FPTfs -- 4.4.1.3 Variable-order Riemann-Liouville pseudo-operational matrix for FPTfs -- 4.4.1.4 Variable-order Riemann-Liouville pseudo-operational matrix for FFWs -- 4.4.2 Extra pseudo-operational matrix of fractional-order Riemann-Liouville integration for fractional-order Fibonacci wavelets -- 4.4.2.1 Extra pseudo-operational matrix of fractional-order Riemann-Liouville integration for FPTfs -- 4.4.2.2 Extra pseudo-operational matrix of fractional-order Riemann-Liouville integration for fractional-order Fibonacci wav... -- 4.5 Description of the computational method -- 4.6 Convergence analysis -- 4.7 Numerical experiments -- 4.8 Conclusions -- References -- 5 Optimization of the approximate solution of the fractional squeezing flow between two infinite plates -- 5.1 Introduction -- 5.2 Mathematical formulation of the problem -- 5.3 Constructing a new family of basis functions -- 5.3.1 The Genocchi polynomials -- 5.3.2 The generalized Genocchi polynomials -- 5.3.3 The operational matrices -- 5.3.4 The function approximation -- 5.4 Description of the method -- 5.5 Convergence analysis of the method -- 5.6 Numerical results -- 5.7 Conclusions -- Conflict of interest -- References -- 6 Multi-parameter generalized fractional operators and their integral transforms -- 6.1 Introduction -- 6.2 Basic concepts -- 6.3 Multi-parameter generalized fractional operators -- 6.4 Examples -- 6.5 Conclusions -- References -- 7 A constructive approach to the fractional Zakharov-Kuznetsov equations of weak nonlinear acoustic ion waves in plasma -- 7.1 Introduction -- 7.2 Preamble -- 7.3 Convergence and error analysis: NITHPM -- 7.4 Constructive approach: NITHPM. | |
| 505 | 8 | |a 7.5 Application of NITHPM -- 7.6 Graphical result and analysis -- 7.7 Conclusions -- References -- 8 Integral formula for matrix factorizations of Helmholtz equation -- 8.1 Introduction -- 8.2 Materials and methods -- 8.2.1 The family of fundamental solutions of the Helmholtz equation -- 8.2.2 Integral formulas in bounded areas -- Declarations -- References -- 9 Cauchy problem for matrix factorizations of Helmholtz equation on a plane -- 9.1 Introduction -- 9.2 The Cauchy problem for matrix factorizations of Helmholtz equation in a two-dimensional bounded domain -- 9.2.1 The integral formula in the type of strip -- 9.2.2 The Cauchy problem for matrix factorizations of the Helmholtz equation in a strip-type domain -- Declarations -- References -- 10 The Cauchy problem for matrix factorizations of Helmholtz equation in space -- 10.1 Introduction -- 10.2 The Cauchy problem for matrix factorizations of the Helmholtz equation in a three-dimensional bounded domain -- 10.3 Integral formula in the layer-type region -- 10.4 Regularization of the Cauchy problem for matrix factorizations of the Helmholtz equation in a layer-type domain -- Declarations -- References -- 11 Modified Newton successive over-relaxation for solving Caputo fractional porous medium equations -- 11.1 Introduction -- 11.2 Time-fractional porous medium equation in Caputo sense -- 11.3 Iterative method and algorithm -- 11.4 Numerical experiment, results, and discussions -- 11.5 Conclusions -- References -- 12 Fractional calculi on time scales: differentiation and integration of a function with respect to another function -- 12.1 Introduction -- 12.2 Preliminaries on time scales -- 12.3 Fractional calculus on time scales of a function with respect to another function -- Acknowledgment -- References. | |
| 505 | 8 | |a 13 Effective strategies to reduce transmission of certain diseases based on their fractional optimal control problems -- 13.1 Introduction -- 13.2 Preliminaries -- 13.2.1 Some basic concepts of FC -- 13.2.2 A general formulation of FOCPs -- 13.3 Results and discussion -- 13.3.1 Formulation of PWD model within FOCP -- 13.3.2 Optimal control strategies for ZVD involving various transmissions -- 13.3.3 FOCP for SIRV model with a combination of vaccination and treatment -- 13.3.4 Prevent the risk of CHD by formulation of FOCP with fish consumption -- 13.4 Conclusions -- References -- 14 Fractional Caputo-type simultaneous scheme for finding all polynomial roots -- 14.1 Introduction -- 14.2 Construction of fractional-type family of numerical scheme -- 14.3 Dynamical analysis -- 14.4 Numerical results -- 14.5 Conclusions -- References -- 15 Application of modified homotopy analysis transform method to fractional modified Kawahara equation -- 15.1 Introduction -- 15.1.1 Fractional modified Kawahara equation -- 15.2 Basic definitions -- 15.3 Novel modified homotopy analysis transform method -- 15.4 Numerical analysis of fractional Kawahara equation using MHATM -- 15.5 Numerical result and discussion -- 15.6 Conclusions -- Acknowledgments -- Funding -- Availability of data and materials -- Conflict of interest -- Authors' contribution -- References -- Index -- Back Cover. | |
| 520 | |a This scholarly work focuses on the recent advancements in fractional calculus and its applications within complex systems. Edited by Praveen Agarwal and other prominent mathematicians, the book provides a comprehensive overview of fractional calculus, emphasizing its role in mathematical modeling and problem-solving across various scientific domains. Key topics include generalized Dirichlet averages, fractional integral inequalities, and the application of Fibonacci wavelets to solve fractional differential equations. It is designed for an audience of researchers, academicians, and professionals engaged in mathematics, engineering, and related fields, aiming to enhance their understanding of modern mathematical techniques and their practical applications in resolving complex scientific challenges. |7 Generated by AI | ||
| 532 | 8 | |a Latest accessibility assessment date: 20250904 | |
| 532 | 8 | |a Accessibility addendum: https://www.elsevier.com/about/accessibility | |
| 532 | 8 | |a Compliance certification by (URL): https://bornaccessible.benetech.org/certified-publishers/ | |
| 532 | 8 | |a Publisher's web page for detailed accessibility information: https://www.elsevier.com/about/accessibility | |
| 532 | 0 | |a Compatibility tested: https://www.elsevier.com/about/accessibility | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibility@elsevier.com | |
| 650 | 0 | |a Fractional calculus. | |
| 650 | 6 | |a Dérivées fractionnaires. |0 (CaQQLa)201-0283840 | |
| 650 | 7 | |a Fractional calculus |2 fast |0 (OCoLC)fst00933515 | |
| 700 | 1 | |a Agarwal, Praveen. | |
| 776 | 0 | 8 | |c Original |z 0443185050 |z 9780443185052 |w (OCoLC)1391432933 |
| 856 | 4 | 0 | |3 ScienceDirect |u https://www.sciencedirect.com/science/book/9780443185052 |