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Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem [article]

Ryan M. Evans, Udita N. Katugampola, David A. Edwards
2016 arXiv   pre-print
In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors  ...  Hence, in this paper we explore the applicability of fractional calculus in real-world applications, further strengthening the true nature of fractional calculus.  ...  Conclusion Recently fractional calculus has been an area that is rich in application. We have found yet another application of fractional calculus in modeling surface-volume reactions.  ... 
arXiv:1510.00408v2 fatcat:s6ahfdn6rrfxvcmgjcytud3uka

Stochastic Models in Reliability

Peng Huang
2000 Technometrics  
Applications of the Calculus of Moving Surfaces.  ...  Integration and Gauss's Theorem.-13. Intrinsic Features of Embedded Surfaces.-14. Further Topics in Differential Geometry.-15. Classical Problems in the Calculus of Variations.-16.  ...  Features 7 First book in the field of matrix models to apply integrable systems to solve the phase transition problems 7 The only book to date to provide a unified model for the densities of eigenvalues  ... 
doi:10.1080/00401706.2000.10486063 fatcat:hinnsdpizzetlndglm64cak2ce

Про Эйлера и Чебышёва, основателей российской математики
On Euler and Chebyshev, at the Foundation of Russian Mathematics

A. Papadopoulos
2021 Успехи кибернетики / Russian Journal of Cybernetics  
continued fractions and number theory, showing that in each filed the two mathematicians were interested in the same kind of questions.  ...  In doing this, I consider the works of Euler and Chebyshev on three topics in applied science: industrial machines, ballistics and geography, and then on three topics in pure mathematics: integration,  ...  Finding a formula for an indefinite integral ∫︀ f is equivalent to solving a differential equation of the type dy/dx = f (x).  ... 
doi:10.51790/2712-9942-2021-2-2-4 fatcat:fs72ib6g6ve57ns4bpkmwnrj54

Book report

2004 Computers and Mathematics with Applications  
Residue Calculus: Poles of Any Order. 82.31 The Residue Theorem. 82.32 Computation of fo 27r R(sin(t), cos(t))dt. 82.33 Computation of fl nfty_copq(~dx. 82.34 Applications to Potential Theory in C 2.  ...  Multiple Integrals. 66.1 Introduction. 66.2 Triple Integrals over the Unit cube. 66.3 Triple Integrals over General Domains in R 3. 66.4 The Volume of a Three-Dimensional Domain. 66.5 Triple Integrals  ... 
doi:10.1016/s0898-1221(04)84016-1 fatcat:szz7sksvhnentlcyspkplxuaya

History of Modern Mathematics

D. E. Smith
1896 Mathematical Gazette  
equations, and the numerous applications of the Newtonian calculus to physical problems.  ...  The Application of the Infinitesimal Calculus to problems in physics and astronomy was contemporary with the origin of the science.  ... 
doi:10.2307/3604091 fatcat:qm7fpamoj5fkpfmbbugomam5oy

1998 International Conference on Mathematical Methods in Electromagnetic Theory - MMET '98

1998 MMET Conference Proceedings. 1998 International Conference on Mathematical Methods in Electromagnetic Theory. MMET 98 (Cat. No.98EX114)  
the collaction of information.  ...  Sand comments regarding this burden estimate or any other aspect of this colection of information, including suggestions for reducing this burden, to Wash Information Operation and Reports. 1215 Jefferson  ...  This work was done with the help of Contract TH 606/96 of the National Science Foundation. Acknowledgment The authors would like to express our gratitude to Prof. B. Bhat and Prof. S. K.  ... 
doi:10.1109/mmet.1998.709792 fatcat:7bqb6g7rdvfxxjo2kmhjqivb2u

The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion [chapter]

Juan Luis Vázquez
2017 Lecture notes in mathematics  
The linear heat equation is the basic mathematical model that has been thoroughly studied in the last two centuries. It was followed by the theory of parabolic equations of different types.  ...  In a parallel development, the theory of stochastic differential equations gives a foundation to the probabilistic study of diffusion.  ...  The text is based on series of lectures given at the CIME Summer School held in Cetraro, Italy, in July 2016. The author is grateful to the CIME foundation for the excellent organization.  ... 
doi:10.1007/978-3-319-61494-6_5 fatcat:suk2jbttnrhpdm3wxeiboeo7qi

The mathematical theories of diffusion. Nonlinear and fractional diffusion [article]

Juan Luis Vázquez
2017 arXiv   pre-print
The linear heat equation is the basic mathematical model that has been thoroughly studied in the last two centuries. It was followed by the theory of parabolic equations of different types.  ...  In a parallel development, the theory of stochastic differential equations gives a foundation to the probabilistic study of diffusion.  ...  The text is based on series of lectures given at the CIME Summer School held in Cetraro, Italy, in July 2016. The author is grateful to the CIME foundation for the excellent organization.  ... 
arXiv:1706.08241v1 fatcat:ecwxw4cbqrc65pluvycbaiurgy

Recent Publications

H. L. Rietz, G. A. Hedlund, Lao G. Simons, H. J. Ettlinger, M. H. Stone, G. T. Whyburn, G. C. Evans, Lester S. Hill
1928 The American mathematical monthly  
famous equation of Abel, with singular kernel, fx) 3 u(t)dt* x) = ae, 0 (x—t)* The treatment includes a brief exposition of methods suitable for this type of equation, with singular and with non-singular  ...  In particular, engineering problems arising in the telephone industry, and important problems of theoret- ical physics, are studied in detail by the methods of the probability calculus.  ... 
doi:10.1080/00029890.1928.11986882 fatcat:vzg2ngwwgvgkzfabu3lna7hj2i

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35] 45E99 None of the above, but in this section 45Fxx Systems of linear integral equations 45F05 Systems of nonsingular  ...  the above, but in this section 44-XX INTEGRAL TRANSFORMS, OPERATIONAL CALCULUS {For fractional derivatives and integrals, see 26A33.  ...  , canonical formalism, Cauchy problems) 83C10 Equations of motion 83C15 Exact solutions 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries 83C22 Einstein-Maxwell equations  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

Review of Simulation Techniques for Aquifer Thermal Energy Storage (ATES) [chapter]

J.W. MERCER, C.R. FAUST, W.J. MILLER, F.J. PEARSON
1982 Advances in Hydroscience  
This code uses a continued fraction formulation and simple iteration to solve its mass balance equations while it used a Newton-Raphson scheme to solve the remaining equations.  ...  Solution Techniques The group of equations which must be solved by mass transfer codes of this type are essentially identical with those solved by ion-association models.  ...  (A-ll) Using the same volume element in Figure A -2, but now considering energy, the components in Equation (A-II) are: (1) Energy transport by convection, that is, energy transferred into the volume  ... 
doi:10.1016/b978-0-12-021813-4.50007-x fatcat:rc4shooienaxrlrdmc3xocqqwm

Looking backward: From Euler to Riemann [article]

Athanase Papadopoulos
2017 arXiv   pre-print
The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration,  ...  We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries.  ...  In the same paper, he presents Abel's addition theorem for elliptic integrals, and he solves Jacobi's inversion problem in terms of p variable magnitudes, for a (2p + 2)-connected surface.  ... 
arXiv:1710.03982v1 fatcat:vnre7wfvybcalafm2hcq5adpji

Looking Backward: From Euler to Riemann [chapter]

Athanase Papadopoulos
2017 From Riemann to Differential Geometry and Relativity  
In the same paper, he presents Abel's addition theorem for elliptic integrals, and he solves Jacobi's inversion problem in terms of p variable magnitudes, for a (2p + 2)-connected surface.  ...  ; this problem he did not succeed in solving except in special cases ...  ... 
doi:10.1007/978-3-319-60039-0_1 fatcat:va7zb3jsprejvbrvbvpacqgp2q

Interfaces and Free Boundaries: Analysis, Control and Simulation

Charles Elliott, Yoshikazu Giga, Michael Hinze, Vanessa Styles
2013 Oberwolfach Reports  
The governing equations for the dynamics of the interfaces in many of these applications involve surface tension expressed in terms of the mean curvature and a driving force.  ...  Often in applications of these mathematical models, suitable performance indices and appropriate control actions have to be specified.  ...  A simple embedding method for solving partial differential equations on surfaces. Journal of Computational Physics 227 (2008), 1943-1961. Part 1 :| 1 Confined sphere-type surfaces.  ... 
doi:10.4171/owr/2013/15 fatcat:fkpzvxt6a5bhdpswg6tyhuxusq

Inversion of Integral Models: a Neural Network Approach [article]

Emilie Chouzenoux, Cecile Della Valle, Jean-Christophe Pesquet
2021 arXiv   pre-print
We apply our method to the inversion of Abel integral operators, which define a fractional integration involved in wide range of physical processes.  ...  We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator.  ...  In a different context, fractional calculus appears to be very convenient to describe properties of polymers [44] or surface-volume reaction problems [45] .  ... 
arXiv:2105.15044v1 fatcat:ijhndcilarcptcwxwtip4v5zda
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