Application of aggregated control functions for approximating $ \mathscr{C} $-Hilfer fractional differential equations

Safoura Rezaei Aderyani; Reza Saadati; Donal O'Regan; Fehaid Salem Alshammari; Safoura Rezaei Aderyani; Reza Saadati; Donal O'Regan; Fehaid Salem Alshammari

doi:10.3934/math.20231433

AIMS Mathematics

2023, Volume 8, Issue 11: 28010-28032. doi: 10.3934/math.20231433

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Research article

Application of aggregated control functions for approximating $ \mathscr{C} $-Hilfer fractional differential equations

1.
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
2.
School of Mathematical and Statistical Sciences, University of Galway, Galway, University Road, H91 TK33 Galway, Ireland
3.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi Arabia

Received: 04 August 2023 Revised: 18 September 2023 Accepted: 21 September 2023 Published: 11 October 2023
MSC : 39B62, 46L05, 46L57, 47B47, 47H10

The main issue we are studying in this paper is that of aggregation maps, which refers to the process of combining various input values into a single output. We apply aggregated special maps on Mittag-Leffler-type functions in one parameter to get diverse approximation errors for fractional-order systems in Hilfer sense using an optimal method. Indeed, making use of various well-known special functions that are initially chosen, we establish a new class of matrix-valued fuzzy controllers to evaluate maximal stability and minimal error. An example is given to illustrate the numerical results by charts and tables.
- aggregation maps,
- special functions,
- stability
Citation: Safoura Rezaei Aderyani, Reza Saadati, Donal O'Regan, Fehaid Salem Alshammari. Application of aggregated control functions for approximating $ \mathscr{C} $-Hilfer fractional differential equations[J]. AIMS Mathematics, 2023, 8(11): 28010-28032. doi: 10.3934/math.20231433

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Abstract

The main issue we are studying in this paper is that of aggregation maps, which refers to the process of combining various input values into a single output. We apply aggregated special maps on Mittag-Leffler-type functions in one parameter to get diverse approximation errors for fractional-order systems in Hilfer sense using an optimal method. Indeed, making use of various well-known special functions that are initially chosen, we establish a new class of matrix-valued fuzzy controllers to evaluate maximal stability and minimal error. An example is given to illustrate the numerical results by charts and tables.

References

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