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Limited frequency band diffusive representation for nabla fractional order transfer functions
2021
Turkish Journal of Mathematics
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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
2019
Mathematics
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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]
2019
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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
2012
Computers and Mathematics with Applications
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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]
2018
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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
2019
Filomat
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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]
2019
arXiv
pre-print
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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?
2022
Nonlinear Analysis: Modelling and Control
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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
2020
Axioms
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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
2017
Discrete Dynamics in Nature and Society
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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
2017
Proceedings of the American Mathematical Society
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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
2012
International Journal of Differential Equations
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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
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