Solutions of Nabla Fractional Difference Equations Using N-Transforms

Mohan, J. Jagan; Deekshitulu, G. V. S. R.

doi:10.1007/s40304-014-0027-9

Cited by 13 publications

(1 citation statement)

References 12 publications

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“…Mathematically, the universality in regular nonlinear dynamics is expressed through the Feigenbaum function and constants (see, e.g., [15,16]), and is based on the analysis of periodic points and their bifurcations. Fractional systems have no bifurcation points [17,18,19,20,21,22,23],…”

Section: Introductionmentioning

confidence: 99%

Bifurcations and transition to chaos in generalized fractional maps of the orders 0 < alpha < 1

Edelman¹,

Helman²,

Smidtaite³

2023

Preprint

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Generalized fractional maps of the orders 0 < α < 1 are Volterra difference equations of convolution type with kernels, which differences are absolutely summable, but the series of kernels are diverging. Commonly used in applications fractional (with the power-law kernels) and fractional difference (with the falling factorial kernels) maps of the orders 0 < α < 1 belong to this class of maps. We derived the algebraic equations which allow the calculation of bifurcation points of generalized fractional maps. We calculated the bifurcation points and drew bifurcation diagrams for the fractional and fractional difference logistic maps. Although the transition to chaos on individual trajectories in fractional maps may be characterized by the cascade of bifurcations type behavior and zero Lyapunov exponents, the results of our numerical simulations allow us to make a conjecture that the cas-

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Section: Introductionmentioning

confidence: 99%

Bifurcations and transition to chaos in generalized fractional maps of the orders 0 < alpha < 1

Edelman¹,

Helman²,

Smidtaite³

2023

Preprint

View full text Add to dashboard Cite

show abstract

Description and analysis of the time–domain response of nabla discrete fractional order systems

Wei

Gao

Cheng

et al. 2020

Asian Journal of Control

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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 function. In particular, we find the limitation of discrete Mittag-Leffler when adopted in describing the response.Then 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 ii) the dynamic behavior of the zero input response. Finally, a simulation study is provided to show the validity of the theoretical results.

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Analysis and description of the infinite-dimensional nature for nabla discrete fractional order systems

Wei

Chen

Wang

et al. 2019

Communications in Nonlinear Science and Numerical Simulation

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Solutions of Nabla Fractional Difference Equations Using N-Transforms

Cited by 13 publications

References 12 publications

Bifurcations and transition to chaos in generalized fractional maps of the orders 0 < alpha < 1

Bifurcations and transition to chaos in generalized fractional maps of the orders 0 < alpha < 1

Description and analysis of the time–domain response of nabla discrete fractional order systems

Analysis and description of the infinite-dimensional nature for nabla discrete fractional order systems

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