Results 91 to 100 of about 611,053 (243)
On some analytic properties of tempered fractional calculus [PDF]
Journal of Computational and Applied Mathematics 366 (2020),
112400, 2019 We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouville fractional calculus and demonstrate how the operators may be used to obtain special functions such as hypergeometric and Appell's functions.
arxiv +1 more source
A new approach on fractional calculus and probability density function
AIMS Mathematics, 2020 In statistical analysis, oftentimes a probability density function is used to describe the relationship between certain unknown parameters and measurements taken to learn about them.
Shu-Bo Chen +4 more
semanticscholar +1 more source
Sturm-Liouville problem in multiplicative fractional calculus
AIMS MathematicsMultiplicative calculus, or geometric calculus, is an alternative to classical calculus that relies on division and multiplication as opposed to addition and subtraction, which are the basic operations of classical calculus.
Tuba Gulsen +3 more
doaj +1 more source
Abelian Groups of Fractional Operators
Computer Sciences & Mathematics Forum, 2022 Taking into count the large number of fractional operators that have been generated over the years, and considering that their number is unlikely to stop increasing at the time of writing this paper due to the recent boom of fractional calculus ...
Anthony Torres-Hernandez +2 more
doaj +1 more source
Definition of fractal measures arising from fractional calculus [PDF]
arXiv, 1998 It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable constructions does offer such a possibility.
arxiv
Fractional Calculus involving (p, q)-Mathieu Type Series
, 2020 Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized (p, q)-Mathieu type series. Then, their composition formulas by using the integral transforms are introduced.
D. Kaur +3 more
semanticscholar +1 more source
Fractional order calculus: historical apologia, basic concepts and some applications
Revista Brasileira de Ensino de FísicaFractional order calculus (FOC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus.
S.A. David +2 more
doaj +1 more source
A conformable fractional calculus on arbitrary time scales
Journal of King Saud University: Science, 2016 A conformable time-scale fractional calculus of order α∈]0,1] is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger time-scale calculus is obtained as a particular case, by choosing α=1.
Nadia Benkhettou +2 more
doaj +1 more source
A new theory of fractional differential calculus [PDF]
arXiv, 2020 This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer order weak derivatives; it also helps to unify multiple existing fractional derivative definitions and characterize
arxiv
Good (and Not So Good) Practices in Computational Methods for Fractional Calculus
Mathematics, 2020 The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order ...
K. Diethelm, R. Garrappa, M. Stynes
semanticscholar +1 more source