Trends, directions for further research, and some open problems of fractional calculus
Sign Up to like & getrecommendations! Published in 2022 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-021-07158-9
Abstract: The 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,… read more here.
Keywords: directions research; fractional calculus; research open; trends directions ... See more keywords
Solutions of the Radial Component of the Fractional Schrödinger Equation Using N-Fractional Calculus Operator
Sign Up to like & getrecommendations! Published in 2020 at "Differential Equations and Dynamical Systems"
DOI: 10.1007/s12591-016-0308-8
Abstract: Fractional calculus tecniques are used for the solutions of some classes of differential equations and fractional differential equations. One of the these tecniques is N-fractional calculus operator $$N^{\eta }$$ N η method. We can obtain… read more here.
Keywords: component fractional; fractional calculus; calculus; radial component ... See more keywords
The solution of certain triple q-integral equations in fractional q-calculus approach
Sign Up to like & getrecommendations! Published in 2019 at "Arab Journal of Mathematical Sciences"
DOI: 10.1016/j.ajmsc.2018.10.001
Abstract: Abstract In this paper, we consider a certain system of triple q -integral equations, where the kernel is the third Jackson q -Bessel functions. We give two solutions by using the fractional q -calculus approach.… read more here.
Keywords: fractional calculus; solution certain; triple integral; integral equations ... See more keywords
NILT and Prony technique for new definitions of fractional calculus for modeling very slow decay phenomena
Sign Up to like & getrecommendations! Published in 2020 at "IFAC-PapersOnLine"
DOI: 10.1016/j.ifacol.2020.12.2053
Abstract: Based on the data from the Tesla users about the degradation of Tesla Model S battery capacity, this paper introduces two new definitions of fractional integrals and derivatives to describe these very slow decay phenomena,… read more here.
Keywords: fractional calculus; decay phenomena; new definitions; definitions fractional ... See more keywords
Estimation of the nitrogen concentration of rubber tree using fractional calculus augmented NIR spectra
Sign Up to like & getrecommendations! Published in 2017 at "Industrial Crops and Products"
DOI: 10.1016/j.indcrop.2017.06.069
Abstract: Abstract Natural rubber ( Hevea brasiliensis ) is a high-valued industrial crop in tropical areas. Reasonable fertilization can improve the quality and production of the natural rubber. Hence, there is a great interest in developing… read more here.
Keywords: using fractional; fractional calculus; rubber tree; rubber ... See more keywords
On the fractional calculus of multivariate Mittag-Leffler functions
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2021.1906869
Abstract: ABSTRACT Multivariate Mittag-Leffler functions are a strong generalisation of the univariate and bivariate Mittag-Leffler functions which are known to be important in fractional calculus. We consider the general functional operator defined by an integral transform… read more here.
Keywords: mittag leffler; leffler functions; fractional calculus; multivariate mittag ... See more keywords
Enhanced Recurrent Fuzzy Neural Fault-Tolerant Synchronization Tracking Control of Multiple Unmanned Airships via Fractional Calculus and Fixed-Time Prescribed Performance Function
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Fuzzy Systems"
DOI: 10.1109/tfuzz.2022.3154441
Abstract: This article proposes a fractional-order intelligent fault-tolerant synchronization tracking control (FO-I-FTSTC) scheme for multiple unmanned airships (UAs) against actuator faults. Within the developed control architecture, fixed-time prescribed performance functions (PPFs) are first designed to transform… read more here.
Keywords: fractional calculus; fuzzy neural; control; synchronization tracking ... See more keywords
THE HADAMARD FRACTIONAL CALCULUS OF A FRACTAL FUNCTION
Sign Up to like & getrecommendations! Published in 2018 at "Fractals"
DOI: 10.1142/s0218348x18500251
Abstract: This paper investigates the Hadamard fractional calculus of a fractal function. It is proved that there exists some linear relationship between the order of Hadamard fractional calculus and the fra... read more here.
Keywords: hadamard fractional; calculus fractal; fractional calculus; fractal function ... See more keywords
TEMPERED FRACTIONAL CALCULUS ON TIME SCALE FOR DISCRETE-TIME SYSTEMS
Sign Up to like & getrecommendations! Published in 2021 at "Fractals"
DOI: 10.1142/s0218348x21400338
Abstract: The fractional derivative holds historical dependence or non-locality and it becomes a powerful tool in many real-world applications. But it also brings error accumulation of the numerical solutions as well as the theoretical analysis since… read more here.
Keywords: tempered fractional; time; fractional calculus; time scale ... See more keywords
A Mathematical Approach with Fractional Calculus for the Modelling of Children's Physical Development
Sign Up to like & getrecommendations! Published in 2019 at "Computational and Mathematical Methods in Medicine"
DOI: 10.1155/2019/3081264
Abstract: From birth to now, it is getting more and more important to keep track of the children development, because knowing and determining the factors related to the physical development of the children would provide better… read more here.
Keywords: mathematical approach; development; fractional calculus; physical development ... See more keywords
Rational Implementation of Fractional Calculus Operator Based on Quadratic Programming
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Problems in Engineering"
DOI: 10.1155/2021/6646718
Abstract: When fractional calculus operators and models are implemented rationally, there exist some problems such as low approximation accuracy of rational approximation function, inability to specify arbitrary approximation frequency band, or poor robustness. Based on the… read more here.
Keywords: quadratic programming; calculus operator; fractional calculus; approximation ... See more keywords