Abstract
In this article, we define a fractional forward discrete operator. Then, for a family of linear nonautonomous fractional difference equations constructed by using this fractional discrete operator, we provide a practical formula of solutions. This family of problems covers several linear fractional difference equations that appear in the literature. Numerical examples are given to justify our theory.
Issue Section:
Research Papers
References
1.
Dassios
,
I.
, 2012
, “
On Non-Homogeneous Generalized Linear Discrete Time Systems
,” Circuits Syst. Signal Process
,
31
(5
), pp. 1699
–1712
.10.1007/s00034-012-9400-72.
Dassios
,
I.
,
Zimbidis
,
A.
, and
Kontzalis
,
C.
, 2014
, “
The Delay Effect in a Stochastic Multiplier–Accelerator Model
,” J. Econ. Struct.
,
3
(1
), p. 7
.10.1186/s40008-014-0007-y3.
Dassios
,
I.
, 2015
, “
Optimal Solutions for Non-Consistent Singular Linear Systems of Fractional Nabla Difference Equations
,” Circuits, Syst. Signal Process.
,
34
(6
), pp. 1769
–1797
.10.1007/s00034-014-9930-24.
DeGroot
,
M. H.
, 1974
, “
Reaching a Consensus
,” J. Am. Stat. Assoc.
,
69
(345
), pp. 118
–121
.10.1080/01621459.1974.104801375.
Ogata
,
K.
, 1987
, Discrete Time Control Systems
,
Prentice Hall
,
New York
.6.
Abadias
,
L.
,
Lizama
,
C.
,
J. Miana
,
P.
, and
Velasco
,
M. P.
, 2019
, “
On Well–Posedness of Vector-Valued Fractional Differential-Difference Equations
,” Discrete Contin. Dyn. Syst.
,
39
(5
), pp. 2679
–2708
.10.3934/dcds.20191127.
Dassios
,
I.
, 2018
, “
A Practical Formula of Solutions for a Family of Linear Non-Autonomous Fractional Nabla Difference Equations
,” J. Comput. Appl. Math
,
339
, pp. 317
–328
.10.1016/j.cam.2017.09.0308.
Klamka
,
J.
, 2010
, “
Controllability and Minimum Energy Control Problem of Fractional Discrete-Time Systems
,” New Trends in Nanotechnology and Fractional Calculus Applications
,
Springer
,
Dordrecht
, The Netherlands, pp. 503
–509
.9.
Rezapour
,
S.
, and
Salehi
,
S.
, 2015
, “
On the Existence of Solution for a k–Dimensional System of Three Points Nabla Fractional Finite Difference Equations
,” Bull. Iranian Math. Soc.
,
41
(6
), pp. 1433
–1444
.http://bims.iranjournals.ir/article_705.html10.
Dassios
,
I.
,
Kerci
,
T.
,
Baleanu
,
D.
, and
Milano
,
F.
, 2023
, “
Fractional–Order Dynamical Model for Electricity Markets
,” Math. Methods Appl. Sci.
,
46
(7
), pp. 8349–8361.10.1002/mma.789211.
Machado
,
J. A.
,
Mata
,
M. E.
, and
Lopes
,
A. M.
, 2015
, “
Fractional State Space Analysis of Economic Systems
,” Entropy
,
17
(12
), pp. 5402
–5421
.10.3390/e1708540212.
Wu
,
G. C.
, and
Baleanu
,
D.
, 2014
, “
Discrete Fractional Logistic Map and Its Chaos
,” Nonlinear Dyn.
,
75
(1–2
), pp. 283
–287
.10.1007/s11071-013-1065-713.
Dassios
,
I.
,
Tzounas
,
G.
, and
Milano
,
F.
, 2023
, Stability Criterion of a Class of Non-Causal Systems of Differential Equations
,
Circuits, Systems and Signal Processing, Vol. 42, Springer
, Berlin
, pp. 2452
–2467
.Copyright © 2023 by ASME
You do not currently have access to this content.