Mittag-Leffler-Type Stability of BAM Neural Networks Modeled by the Generalized Proportional Riemann–Liouville Fractional Derivative
The main goal of the paper is to use a generalized proportional Riemann–Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved, such as the fractional derivative of a squa...
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MDPI AG
2023-06-01
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| Online Access: | https://www.mdpi.com/2075-1680/12/6/588 |
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| author | Ravi P. Agarwal Snezhana Hristova Donal O’Regan |
| author_facet | Ravi P. Agarwal Snezhana Hristova Donal O’Regan |
| author_sort | Ravi P. Agarwal |
| collection | DOAJ |
| description | The main goal of the paper is to use a generalized proportional Riemann–Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved, such as the fractional derivative of a squared function. Additionally, some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time, the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given, illustrating the meaning of the equilibrium as well as its stability properties. |
| first_indexed | 2024-03-11T02:46:53Z |
| format | Article |
| id | doaj.art-88dc58f622a8481aaebfb5e39828e8fd |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T02:46:53Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-88dc58f622a8481aaebfb5e39828e8fd2023-11-18T09:17:09ZengMDPI AGAxioms2075-16802023-06-0112658810.3390/axioms12060588Mittag-Leffler-Type Stability of BAM Neural Networks Modeled by the Generalized Proportional Riemann–Liouville Fractional DerivativeRavi P. Agarwal0Snezhana Hristova1Donal O’Regan2Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USAFaculty of Mathematics and Informatics, Plovdiv University, Tzar Asen 24, 4000 Plovdiv, BulgariaSchool of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, IrelandThe main goal of the paper is to use a generalized proportional Riemann–Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved, such as the fractional derivative of a squared function. Additionally, some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time, the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given, illustrating the meaning of the equilibrium as well as its stability properties.https://www.mdpi.com/2075-1680/12/6/588BAM neural networksMittag-Leffler-type stabilityfractional differential equationsgeneralized proportional Riemann–Liouville fractional derivative |
| spellingShingle | Ravi P. Agarwal Snezhana Hristova Donal O’Regan Mittag-Leffler-Type Stability of BAM Neural Networks Modeled by the Generalized Proportional Riemann–Liouville Fractional Derivative Axioms BAM neural networks Mittag-Leffler-type stability fractional differential equations generalized proportional Riemann–Liouville fractional derivative |
| title | Mittag-Leffler-Type Stability of BAM Neural Networks Modeled by the Generalized Proportional Riemann–Liouville Fractional Derivative |
| title_full | Mittag-Leffler-Type Stability of BAM Neural Networks Modeled by the Generalized Proportional Riemann–Liouville Fractional Derivative |
| title_fullStr | Mittag-Leffler-Type Stability of BAM Neural Networks Modeled by the Generalized Proportional Riemann–Liouville Fractional Derivative |
| title_full_unstemmed | Mittag-Leffler-Type Stability of BAM Neural Networks Modeled by the Generalized Proportional Riemann–Liouville Fractional Derivative |
| title_short | Mittag-Leffler-Type Stability of BAM Neural Networks Modeled by the Generalized Proportional Riemann–Liouville Fractional Derivative |
| title_sort | mittag leffler type stability of bam neural networks modeled by the generalized proportional riemann liouville fractional derivative |
| topic | BAM neural networks Mittag-Leffler-type stability fractional differential equations generalized proportional Riemann–Liouville fractional derivative |
| url | https://www.mdpi.com/2075-1680/12/6/588 |
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