Variable-order fractional discrete-time recurrent neural networks

The aim of this study is to develop a transform method for discrete calculus. We define the double Laplace transforms in a discrete setting and discuss its existence and uniqueness with some of its important properties. The delta double Laplace transforms have been presented for integer and noninteger order partial differences. For illustration, the delta double Laplace transforms are applied to solve partial difference equation.

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“…Definition 5 (see [10]). Assume f, g: N a ⟶ R. e convolution product is defined by (12) Note that by the empty sum convention (f * g)(a) � 0.…”

Section: { } and N Bmentioning

confidence: 99%

“…For difference equations, Bohner and Peterson treat the dynamic equations on time scales in [2] and get surprisingly different results from continuous counterpart. Some results can be found in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] which has helped to construct the theory of discrete fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale

Haider

Rehman

Abdeljawad

2020

Mathematical Problems in Engineering

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“…erefore, its improvement such as the introduction of fractional-order calculus is needed. e variable-order fractional discrete-time neural network was proposed [10]. A fractional-order complex-valued RNN was designed [11].…”

Section: Introductionmentioning

confidence: 99%

Vessel Track Prediction Based on Fractional Gradient Recurrent Neural Network with Maneuvering Behavior Identification

Han

Chai

2021

Scientific Programming

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To improve the accuracy of ship track prediction, a fractional-order gradient descent method is adopted into a recurrent neural network (RNN). The convergence of the proposed algorithm is proved. Identification of ship maneuvering behavior, atmospheric information, and oceanographic information is considered in vessel tack prediction. The ship track of Xiamen Port is predicted using the new algorithm. Error analysis is made with different factional orders and traffic busy degrees. Results show that the testing and training error differs with different fractional orders. The predicted track results can not only improve the efficiency of marine traffic management but also prevent and warn the safety accidents, so as to avoid accidents.

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“…A few years earlier, fractional differential equations and dynamic systems have been validated as being significant gadgets in showing a few marvels in different parts of applied and pure sciences. They draw enormous importance in research-oriented fields (see the basic monograph and the interesting paper [3,4]. The set of implications that encouraged the formation of a discrete fractional theory is established [5].…”

Section: Introduction and Essentialsmentioning

confidence: 99%

Discrete Fractional Inequalities Pertaining a Fractional Sum Operator with Some Applications on Time Scales

Khan

Shah

2021

Journal of Function Spaces

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This content replicates some discrete nonlinear fractional inequalities by virtue of the fractional sum operator Ψ ¯ on time scales. Through the recognition of the principle of discrete fractional calculus, we are able to recover the precise estimates for unknown functions of inequalities of the Gronwall type. The resultant inequalities are of unique structure comparative with the latest reviewing disclosures and can be described as a complementary tool for numerically testing the solutions of discrete partial differential equations. The foremost consequences are probably confirmed via handling of assessment procedure and technique of mean value speculation. We display few examples of the proposed inequalities to represent the incentives of our effort.

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Variable-order fractional discrete-time recurrent neural networks

Cited by 135 publications

References 22 publications

A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale

A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale

Vessel Track Prediction Based on Fractional Gradient Recurrent Neural Network with Maneuvering Behavior Identification

Discrete Fractional Inequalities Pertaining a Fractional Sum Operator with Some Applications on Time Scales

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