Filters








98 Hits in 3.1 sec

Limited frequency band diffusive representation for nabla fractional order transfer functions

2021 Turkish Journal of Mathematics  
Afterwards, the limited frequency band diffusive representation and the unit impulse response are derived for a series of nabla fractional order transfer functions.  ...  Under this background, this paper concerns the diffusive representation of nabla fractional order systems.  ...  Acknowledgment The work described in this paper was fully supported by the National Natural Science Foundation of China (61601431), the Anhui Provincial Natural Science Foundation (1708085QF141), the Fundamental  ... 
doi:10.3906/mat-2105-87 fatcat:4gbm4nj7znfd3jdapdefqp2ipm

On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels

Thabet Abdeljawad, Arran Fernandez
2019 Mathematics  
The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag–Leffler kernels. The iteration process depends on the binomial theorem.  ...  We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math7090772 fatcat:wbxobzws7vdfvd2sgifgurmv34

On a new class of fractional difference-sum operators based on discrete Atangana-Baleanu sums [article]

Thabet Abdeljawad, Arran Fernandez
2019 arXiv   pre-print
The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag-Leffler kernels. The iteration process depends on the binomial theorem.  ...  We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms.  ...  The second author would like to thank the Engineering and Physical Sciences Research Council (EPSRC) for their support in the form of a research student grant.  ... 
arXiv:1901.08268v1 fatcat:xj7ivd5vq5brnkxbi6rqyu4wdy

Analytical and numerical representations for discrete Grunwald-Letnikov fractional calculus [article]

Yiheng Wei, Tianyu Liu, Peter W Tse, Yong Wang
2019 arXiv   pre-print
This paper focuses on the new representation of Grunwald-Letnikov discrete fractional calculus.  ...  By resorting the classical nabla Taylor series, the series representation of Grunwald-Letnikov difference/sum is established.  ...  To avoid the calculation of infinite series, Granger and Joyeux proposed a more useful version of discrete fractional calculus in [9] , where the infinite series was replaced by a finite one.  ... 
arXiv:1901.09211v1 fatcat:e6lkp7zsrjem7obwc5bp2gcyhq

Gronwall's inequality on discrete fractional calculus

Ferhan M. Atıcı, Paul W. Eloe
2012 Computers and Mathematics with Applications  
Then we give an explicit solution to the linear discrete fractional sum equation. This allows us to state and prove an analogue of Gronwall's inequality on discrete fractional calculus.  ...  As a result, we obtain Gronwall's inequality for discrete calculus with the nabla operator.  ...  Notations and basics of nabla fractional calculus Let a ∈ R and let ν > 0.  ... 
doi:10.1016/j.camwa.2011.11.029 fatcat:j4y4amntrzgpxbjn4g32nxkhha

Time-domain response of nabla discrete fractional order systems [article]

Yiheng Wei, Qing Gao, Songsong Cheng, Yong Wang
2018 arXiv   pre-print
This paper investigates the time--domain response of nabla discrete fractional order systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag--Leffler  ...  In particular, we establish two fundamental properties of a nabla discrete fractional order system with nonzero initial instant: i) the existence and uniqueness of the system time--domain response; and  ...  Acknowledgements The work described in this paper was supported by the National Natural Science Foundation of China (61601431, 61573332), the Anhui Provincial Natural Science Foundation (1708085QF141),  ... 
arXiv:1812.11370v1 fatcat:fa5q5zgucnaehj6ojvyo6tqgu4

Existence and Uniqueness of Solutions of Nabla Fractional Difference Equations Tending to a Nonnegative Constant [article]

Raziye Mert, Allan Peterson, Thabet Abdeljawad, Lynn Erbe
2018 arXiv   pre-print
In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem to be incomplete.  ...  This study was supported by The Scientific and Technological Research Council of Turkey while the first author visiting the University of Nebraska-Lincoln.  ...  The third author would like to thank Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.  ... 
arXiv:1803.03170v1 fatcat:tljgnwaw25aytbihkz5tvvnm4m

Analytical calculation of the inverse nabla Laplace transform [article]

Yiheng Wei, YangQuan Chen, Yuquan Chen, Yong Wang
2019 arXiv   pre-print
For the second method, a table on the transform pairs of those popular functions is carefully established.  ...  The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered.  ...  Afterwards, several novel properties were derived and then applied in the nabla fractional calculus (see Chapter 3 of the famous monograph [12] ).  ... 
arXiv:1909.02655v2 fatcat:4ilyamemhbghjhfhkfhlaqtke4

Generalized quantum exponential function and its applications

Burcu Silindir, Ahmet Yantir
2019 Filomat  
We state (q,h)-analogue of Taylor series and introduce generalized quantum exponential function which is determined by Taylor series in generalized quantum binomial.  ...  We conclude that both representations of generalized quantum exponential function are equivalent. We illustrate our results by ordinary and partial difference equations.  ...  Acknowledgement This article is dedicated to the memory of my beloved mother Müjgan Silindir.  ... 
doi:10.2298/fil1915907s fatcat:37kjszoebzb6bdxh7crpnkwh2e

Hölderian convergence of fractional extended nabla operator to fractional derivative [article]

L. Khitri-Kazi-Tani, H.Dib
2019 arXiv   pre-print
In this paper, we construct the fractional extended nabla operator as fractional power of linear spline of backward difference operator.  ...  Then we prove the strong convergence of this operator to fractional derivative in a H\"older space setting. Finally numerical examples are presented.  ...  The discrete calculus provides a natural setting to define such operators.  ... 
arXiv:1904.06884v1 fatcat:hjqyoe6jszfjzganm646lxndwm

How to empower Grünwald–Letnikov fractional difference equations with available initial condition?

Yiheng Wei, Jinde Cao, Chuang Li, Yangquan Chen
2022 Nonlinear Analysis: Modelling and Control  
In this paper, the initial condition independence property of Grünwald–Letnikov fractional difference is revealed for the first time.  ...  Armed with this information, the concerned property is examined on three modified Grünwald–Letnikov definitions.  ...  Section 2 introduces some basic knowledge of nabla discrete fractional calculus.  ... 
doi:10.15388/namc.2022.27.26623 fatcat:fa4hmc726fduxeo5h3t5iuxiua

Differential and Difference Equations: A Themed Issue Dedicated to Prof. Hari M. Srivastava on the Occasion of His 80th Birthday

Sotiris K. Ntouyas
2020 Axioms  
Differential and difference equations play an important role in many branches of mathematics [...]  ...  In addition, they prove a fundamental theorem of nabla integral calculus for fuzzy functions on time scales under generalized differentiability on time scales.  ...  • The authors of [16] , introduce and study a new derivative called generalized nabla derivative for fuzzy functions on time scales via Hukuhara difference and studies some basic properties.  ... 
doi:10.3390/axioms9040135 fatcat:rukpg73xfrf5xcxlzrtbe32s5u

Existence Results for Fractional Hahn Difference and Fractional Hahn Integral Boundary Value Problems

Nichaphat Patanarapeelert, Thanin Sitthiwirattham
2017 Discrete Dynamics in Nature and Society  
The existence and uniqueness results of two fractional Hahn difference boundary value problems are studied.  ...  The Banach fixed-point theorem and the Schauder fixed-point theorem are used as tools to prove the existence and uniqueness of solution of the problems.  ...  Acknowledgments This research was funded by King Mongkut's University of Technology North Bangkok (Contract no. KMUTNB-GOV-60-76).  ... 
doi:10.1155/2017/7895186 fatcat:ormhxhtmw5g75d67a4qthvtefm

The Poisson distribution, abstract fractional difference equations, and stability

Carlos Lizama
2017 Proceedings of the American Mathematical Society  
We show how several properties for fractional differences, including their own definition, are connected with the continuous case by means of sampling using the Poisson distribution.  ...  We introduce a method based on the Poisson distribution to show existence and qualitative properties of solutions for the problem (*), using operator-theoretical conditions on A.  ...  Grey and Zhang [27] developed a fractional calculus for the discrete nabla (backward) difference operator.  ... 
doi:10.1090/proc/12895 fatcat:t65z5fl3snenvox4qoo3jjcqse

Fractional Order Difference Equations

J. Jagan Mohan, G. V. S. R. Deekshitulu
2012 International Journal of Differential Equations  
A difference equation is a relation between the differences of a function at one or more general values of the independent variable.  ...  These equations usually describe the evolution of certain phenomena over the course of time. The present paper deals with the existence and uniqueness of solutions of fractional difference equations.  ...  Now we introduce some basic definitions and results concerning nabla discrete fractional calculus. Definition 2.1.  ... 
doi:10.1155/2012/780619 fatcat:ihklktmrfjf2xbs36mytwxtr6i
« Previous Showing results 1 — 15 out of 98 results