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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2020.1
- 수록면
- 73 - 116 (44page)
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The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operator of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional “differintegral” equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.
#fractional calculus
#fractional-order integrals
#fractional-order derivatives
#differential equations
#Integral equations
#Cauchy-Goursat integral formula
#differintegral equations
#special functions
#mathematical physics
#Fuchsian and nonFuchsian differential equations
#fractional kinetic equations
#Laplace and Sumudu transforms
#Mittag-Leffler type functions
#fractional integral operators
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참고문헌 (112)
참고문헌 신청
A. Alsaedi / 2016 / On coupled systems of timefractional differential problems by using a new fractional derivative / J. Funct. Spaces :8
M. A. Asiru / 2001 / Sumudu transform and the solution of integral equations of convolution type / Internat. J. Math. Ed. Sci. Tech 32:906~910
A. Atangana / 2016 / On the new fractional derivative and application to nonlinear Fisher’s reaction diffusion equation / Appl. Math. Comput 273:948~956
A. Atangana / 2015 / Extension of the RLC electrical circuit to fractional derivative without singular kernel / Adv. Mech. Engrg 7(6):1~6
A. Atangana / 2015 / Analysis of the Keller-Segel model with a fractional derivative without singular kernel / Entropy 17:4439~4453
M. A. Asiru / 2001 / Sumudu transform and the solution of integral equations of convolution type / Internat. J. Math. Ed. Sci. Tech 32:906~910
A. Atangana / 2016 / On the new fractional derivative and application to nonlinear Fisher’s reaction diffusion equation / Appl. Math. Comput 273:948~956
A. Atangana / 2015 / Extension of the RLC electrical circuit to fractional derivative without singular kernel / Adv. Mech. Engrg 7(6):1~6
A. Atangana / 2015 / Analysis of the Keller-Segel model with a fractional derivative without singular kernel / Entropy 17:4439~4453
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