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

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*. ...

##
###
Stochastic Models in Reliability

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 ...

##
###
Про Эйлера и Чебышёва, основателей российской математики

On Euler and Chebyshev, at the Foundation of Russian Mathematics

2021
*
Успехи кибернетики / Russian Journal of Cybernetics
*

On Euler and Chebyshev, at the Foundation of Russian Mathematics

continued

doi:10.51790/2712-9942-2021-2-2-4
fatcat:fs72ib6g6ve57ns4bpkmwnrj54
*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). ...##
###
Book report

2004
*
Computers and Mathematics with Applications
*

Residue

doi:10.1016/s0898-1221(04)84016-1
fatcat:szz7sksvhnentlcyspkplxuaya
*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*...##
###
History of Modern Mathematics

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. ...

##
###
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

doi:10.1109/mmet.1998.709792
fatcat:7bqb6g7rdvfxxjo2kmhjqivb2u
*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. ...##
###
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion
[chapter]

2017
*
Lecture notes in mathematics
*

The linear heat

doi:10.1007/978-3-319-61494-6_5
fatcat:suk2jbttnrhpdm3wxeiboeo7qi
*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. ...##
###
The mathematical theories of diffusion. Nonlinear and fractional diffusion
[article]

2017
*
arXiv
*
pre-print

The linear heat

arXiv:1706.08241v1
fatcat:ecwxw4cbqrc65pluvycbaiurgy
*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. ...##
###
Recent Publications

1928
*
The American mathematical monthly
*

famous

doi:10.1080/00029890.1928.11986882
fatcat:vzg2ngwwgvgkzfabu3lna7hj2i
*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*. ...##
###
Fourier's Method of Linear Programming and Its Dual

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*...

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

1982
*
Advances in Hydroscience
*

This code uses a continued

doi:10.1016/b978-0-12-021813-4.50007-x
fatcat:rc4shooienaxrlrdmc3xocqqwm
*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*...##
###
Looking backward: From Euler to Riemann
[article]

2017
*
arXiv
*
pre-print

The subjects discussed include the theory

arXiv:1710.03982v1
fatcat:vnre7wfvybcalafm2hcq5adpji
*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*. ...##
###
Looking Backward: From Euler to Riemann
[chapter]

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 ... ...

##
###
Interfaces and Free Boundaries: Analysis, Control and Simulation

2013
*
Oberwolfach Reports
*

The governing

doi:10.4171/owr/2013/15
fatcat:fkpzvxt6a5bhdpswg6tyhuxusq
*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*. ...##
###
Inversion of Integral Models: a Neural Network Approach
[article]

2021
*
arXiv
*
pre-print

We apply our method to the inversion

arXiv:2105.15044v1
fatcat:ijhndcilarcptcwxwtip4v5zda
*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] . ...
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