Discrete Fractional‐Order BAM Neural Networks with Leakage Delay: Existence and Stability Results

Abstract

In this paper, a discrete model of fractional-order bidirectional associative memory (BAM) neural networks with leakage delay is considered. Sufficient conditions are established for the existence, uniqueness and uniform stability of nontrivial solutions of the addressed model. Our approach is based on the implementation of the newly defined discrete fractional calculus, mathematical inequalities and fixed point theorems. We provide an example that supports the application of the theoretical results.

Green–Haar wavelets method for generalized fractional differential equations

“…The fractional operators in (4) and (5) represent Caputo and Caputo-Hadamard fractional derivative, respectively.…”

“…and 3.00445 × 10 -7 1.25591 × 10 -7 1.99284 × 10 -8 0.3 1.09542 × 10 - 5 9.66989 × 10 -6 1.55214 × 10 -6 8.73622 × 10 -7 0.5 5.35004 × 10 - 5 3.25183 × 10 -5 1.55037 × 10 -5 6.56296 × 10 -6 0.7 2.80508 × 10 - 4 1.31354 × 10 -4 5.49232 × 10 -5 2.15731 × 10 -5 0.9 6.65574 × 10 - 4 3.15256 × 10 -4 1.11750 × 10 -4 2.89674 × 10 -5…”

“…These applications of fractional calculus have been elaborated previously by several authors. In essence, fractional calculus has been deployed for modeling the transfer of heat in heterogeneous media [1], nonlinear oscillation of earthquakes [2], signal processing [3], neural networks [4][5][6], fluid dynamic traffic flow [7], electromagnetism [8], bioengineering [9], economics [10], anomalous diffusions and fractal-like nature [11,12]. For the qualitative analysis of fractional differential equations, we refer the reader to [1,2,[13][14][15] and the references therein.…”

Approximate Controllability of Fractional Nonlinear Hybrid Differential Systems via Resolvent Operators

“…Fractional differential systems have described many practical dynamical phenomena more efficiently than the corresponding integer-order systems; hence they have attracted the attention of many researchers in such fields (see [1][2][3][4][5][6][7][8][9][10] and references cited therein).…”

On stability analysis of semi‐linear fractional differential systems

“…Fractional differential systems have attracted the attention of many researchers in many applicable disciplines since the fractional derivatives are considered more appropriate than the corresponding classical integer-ordered derivatives (see previous studies [1][2][3][4][5][6][7] and references therein).…”