fractional calculus
Recently Published Documents


TOTAL DOCUMENTS

1853
(FIVE YEARS 563)

H-INDEX

81
(FIVE YEARS 14)

10.1142/12743 ◽  
2022 ◽  
Author(s):  
Trifce Sandev ◽  
Alexander Iomin

2022 ◽  
Vol 40 ◽  
pp. 1-14
Author(s):  
Shigeyoshi Owa ◽  
Mohamed Kamal Aouf ◽  
Hanaa Zayed

In this paper we introduce and study new classes VM_{p,η}(λ,α,β) and VN_{p,η}(λ,α,β) of multivalent functions with varying arguments of coefficients. We obtain coefficients inequalities, distortion theorems and extreme points for functions in these classes. Also, we investigate several distortion inequalities involving fractional calculus. Finally, results on partial sums are considerd.


Author(s):  
Kai Diethelm ◽  
Virginia Kiryakova ◽  
Yuri Luchko ◽  
J. A. Tenreiro Machado ◽  
Vasily E. Tarasov

AbstractThe area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or, at least, the challenges identified in the scope of advanced research works. This paper gives a vision about the directions for further research as well as some open problems of FC. A number of topics in mathematics, numerical algorithms and physics are analyzed, giving a systematic perspective for future research.


2022 ◽  
Vol 2022 ◽  
pp. 1-7
Author(s):  
Erjian Wei ◽  
Bin Hu ◽  
Jing Li ◽  
Kai Cui ◽  
Zhen Zhang ◽  
...  

A rock creep constitutive model is the core content of rock rheological mechanics theory and is of great significance for studying the long-term stability of engineering. Most of the creep models constructed in previous studies have complex types and many parameters. Based on fractional calculus theory, this paper explores the creep curve characteristics of the creep elements with the fractional order change, constructs a nonlinear viscoelastic-plastic creep model of rock based on fractional calculus, and deduces the creep constitutive equation. By using a user-defined function fitting tool of the Origin software and the Levenberg–Marquardt optimization algorithm, the creep test data are fitted and compared. The fitting curve is in good agreement with the experimental data, which shows the rationality and applicability of the proposed nonlinear viscoelastic-plastic creep model. Through sensitivity analysis of the fractional order β2 and viscoelastic coefficient ξ2, the influence of these creep parameters on rock creep is clarified. The research results show that the nonlinear viscoelastic-plastic creep model of rock based on fractional calculus constructed in this paper can well describe the creep characteristics of rock, and this model has certain theoretical significance and engineering application value for long-term engineering stability research.


2022 ◽  
pp. 441-482
Author(s):  
Agniv Tapadar ◽  
Farooq Ahmad Khanday ◽  
Siddhartha Sen ◽  
Avishek Adhikary

2022 ◽  
Vol 40 ◽  
pp. 1-10
Author(s):  
Dinesh Kumar ◽  
Frederic Ayant

In this paper we study a pair of unied and extended fractional integral operator involving the multivariable Aleph-function, Aleph-function and general class of polynomials. During this study, we establish ve theorems pertaining to Mellin transforms of these operators. Furthers, some properties of these operators have also been investigated. On account of the general nature of the functions involved herein, a large number of (known and new) fractional integral operators involved simpler functions can also be obtained . We will quote the particular case concerning the multivariable I-function dened by Sharma and Ahmad [20] and the I-function of one variable dened by Saxena [13].


2022 ◽  
pp. 513-549
Author(s):  
Meryeme Hassouna ◽  
El Hassan El Kinani ◽  
Abdelaziz Ouhadan
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document