Atnaujinkite slapukų nuostatas

El. knyga: Lie Symmetry Analysis of Fractional Differential Equations [Taylor & Francis e-book]

(Cankaya University, Turkey),
  • Formatas: 222 pages
  • Išleidimo metai: 10-Jul-2020
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-13: 9781003008552
Kitos knygos pagal šią temą:
  • Taylor & Francis e-book
  • Kaina: 240,04 €*
  • * this price gives unlimited concurrent access for unlimited time
  • Standartinė kaina: 342,91 €
  • Sutaupote 30%
Lie Symmetry Analysis of Fractional Differential EquationsDidesnis paveikslėlis
  • Formatas: 222 pages
  • Išleidimo metai: 10-Jul-2020
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-13: 9781003008552
Kitos knygos pagal šią temą:
Taylor & Francis e-booksMore info about Taylor & Francis e-books
Partnerių interneto svetainė: https://www.taylorfrancis.com/books/9781003008552
The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications.

It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications.

In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations.

Features











Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications





Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries





Filled with various examples to aid understanding of the topics
Preface xi
Authors xiii
1 Lie symmetry analysis of integer order differential equations
1(74)
1.1 Classical Lie symmetry analysis
1(39)
1.1.1 Lie symmetries of the Fornberg-Whitham equation
4(1)
1.1.1.1 Similarity reductions and exact solutions
5(3)
1.1.2 Lie symmetries of the modified generalized Vakhnenko equation
8(9)
1.1.3 Lie symmetries of the Magneto-electro-elastic circular rod equation
17(5)
1.1.4 Lie symmetries of the couple stress fluid-filled thin elastic tubes
22(5)
1.1.5 Lie symmetries of the generalized Kadomtsev-Petviashvili-modified equal width equation
27(7)
1.1.6 Lie symmetries of the mKdV-KP equation
34(6)
1.2 Nonclassical Lie symmetry analysis
40(19)
1.2.1 Nonclassical symmetries for a class of reaction-diffusion equations
40(1)
1.2.1.1 Heir-equations and nonclassical symmetries
41(5)
1.2.1.2 R(u, x) = -1/2x2u3 + 3u2 + 1/2c2u
46(1)
1.2.1.3 R(u, x) = -1/2ecxu3 +c2/4 u + ecx/2
46(7)
1.2.2 Nonclassical symmetries of the Black-Scholes equation
53(6)
1.3 Self-adjointness and conservation laws
59(16)
1.3.1 Conservation laws of the Black-Scholes equation
62(5)
1.3.2 Conservation laws of the couple stress fluid-filled thin elastic tubes
67(3)
1.3.3 Conservation laws of the Fornberg-Whitham equation
70(2)
1.3.4 Conservation laws of the mKdV-KP equation
72(3)
2 Group analysis and exact solutions of fractional partial differential equations
75(38)
2.1 Basic theory of fractional differential equations
75(5)
2.2 Group analysis of fractional differential equations
80(2)
2.3 Group analysis of time-fractional Fokker-Planck equation
82(5)
2.3.1 Exact solutions of time-fractional Fokker-Planck equation by invariant subspace method
85(2)
2.4 Lie symmetries of time-fractional Fisher equation
87(4)
2.5 Lie symmetries of time-fractional K(m, n) equation
91(2)
2.6 Lie symmetries of time-fractional gas dynamics equation
93(1)
2.7 Lie symmetries of time-fractional diffusion-absorption equation
94(3)
2.7.1 Exact solutions of time-fractional diffusion-absorption by invariant subspace method
96(1)
2.8 Lie symmetries of time-fractional Clannish Random Walker's parabolic equation
97(2)
2.8.1 Exact solutions of time-fractional Clannish Random Walker's equation by invariant subspace method
98(1)
2.9 Lie symmetries of the time-fractional Kompaneets equation
99(4)
2.10 Lie symmetry analysis of the time-fractional variant Boussinesq and coupled Boussinesq-Burger's equations
103(10)
2.10.1 Exact solutions of time-fractional VB and BB equations by invariant subspace method
109(4)
3 Analytical Lie group approach for solving the fractional integro-differential equations
113(16)
3.1 Lie groups of transformations for FIDEs
114(1)
3.2 The invariance criterion for FIDEs
114(5)
3.3 Symmetry group of FIDEs
119(3)
3.4 Kernel function, free term and related symmetry group of the FIDEs
122(7)
3.4.1 General conditions for K and J
122(1)
3.4.2 Some special cases
123(6)
4 Nonclassical Lie symmetry analysis to fractional differential equations
129(30)
4.1 General solutions extracted from invariant surfaces to fractional differential equations
131(15)
4.1.1 Fractional diffusion equation
139(2)
4.1.2 Fractional Burger's equation
141(1)
4.1.3 Fractional Airy's equation
142(2)
4.1.4 Fractional KdV equation
144(1)
4.1.5 Fractional gas dynamic equation
145(1)
4.2 Lie symmetries of space fractional diffusion equations
146(3)
4.2.1 Nonclassical method
147(2)
4.3 Lie symmetries of time-fractional diffusion equation
149(4)
4.3.1 Nonclassical method
150(3)
4.4 General solutions to fractional diffusion equations by invariant surfaces
153(6)
5 Conservation laws of the fractional differential equations
159(28)
5.1 Description of approach
160(13)
5.1.1 Time-fractional diffusion equations
160(1)
5.1.2 Conservation laws and nonlinear self-adjointness
160(2)
5.1.3 Fractional Noether operators
162(2)
5.1.4 Nonlinear self-adjointness of linear TFDE
164(1)
5.1.5 Conservation laws for TFDE with the Riemann--Liouville fractional derivative
165(1)
5.1.6 Conservation laws for TFDE with the Caputo fractional derivative
166(1)
5.1.7 Symmetries and nonlinear self-adjointness of nonlinear TFDE
167(1)
5.1.8 Conservation laws for nonlinear TFDE with the Riemann--Liouville fractional derivative
168(1)
5.1.9 Conservation laws for nonlinear TFDE with the Caputo fractional derivative
169(4)
5.2 Conservation laws of fractional diffusion-absorption equation
173(1)
5.3 Nonlinear self-adjointness of the Kompaneets equations
174(8)
5.3.1 Conservation laws for approximations of the Eq. (2.82)
177(1)
5.3.2 Conservation laws for approximations of the Eq. (2.84)
178(1)
5.3.3 Conservation laws for approximations of the Eq. (2.85)
179(1)
5.3.4 Conservation laws for approximations of the Eq. (2.86)
180(1)
5.3.5 Noninvariant particular solutions
181(1)
5.4 Conservation laws of the time-fractional CRW equation
182(1)
5.5 Conservation laws of the time-fractional VB equation and time-fractional BB equation
183(4)
5.5.1 Construction of conservation laws for Eq. (5.91)
185(2)
Bibliography 187(16)
Index 203
Mir Sajjad Hashemi is associate professor at the University of Bonab, Iran. His field of interests include the fractional differential equations, Lie symmetry method, Geometric integration, Approximate and analytical solutions of differential equations and soliton theory.

Dumitru Baleanu is professor at the Institute of Space Sciences, Magurele-Bucharest, Romania and visiting staff member at the Department of Mathematics, Cankaya University, Ankara, Turkey. His field of interests include the fractional dynamics and its applications in science and engineering, fractional differential equations, discrete mathematics, mathematical physics, soliton theory, Lie symmetry, dynamic systems on time scales and the wavelet method and its applications.
Pastovi nuoroda: https://www.kriso.lt/db/9781003008552_pe.html
Raktažodžiai: