A computational method for investigating a quantum integrodifferential inclusion with simulations and heatmaps

Shahram Rezapour; Sabri T. M. Thabet; Imed Kedim; Miguel Vivas-Cortez; Mehran Ghaderi; Shahram Rezapour; Sabri T. M. Thabet; Imed Kedim; Miguel Vivas-Cortez; Mehran Ghaderi

doi:10.3934/math.20231394

AIMS Mathematics

2023, Volume 8, Issue 11: 27241-27267. doi: 10.3934/math.20231394

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Research article

A computational method for investigating a quantum integrodifferential inclusion with simulations and heatmaps

1.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
3.
Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen
4.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
5.
Escuela de Ciencias Fisicas y Matematicas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Catolica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador

Received: 07 August 2023 Revised: 26 August 2023 Accepted: 03 September 2023 Published: 25 September 2023
MSC : 34A08, 34A12

We aim to investigate an integro-differential inclusion using a novel computational approach in this research. The use of quantum calculus, and consequently the creation of discrete space, allows the computer and computational algorithms to solve our desired problem. Furthermore, to guarantee the existence of the solution, we use the endpoint property based on fixed point methods, which is one of the most recent techniques in fixed point theory. The above will show the novelty of our work, because most researchers use classical fixed point techniques in continuous space. Moreover, the sensitivity of the parameters involved in controlling the existence of the solution can be recognized from the heatmaps. For a better understanding of the issue and validation of the results, we presented numerical algorithms, tables and some figures in our examples that are presented at the end of the work.
- fractional calculus,
- endpoint property,
- Pompieu-Hausdorff metric,
- boundary value problem,
- integro-differential inclusion,
- quantum calculus,
- fixed point theory
Citation: Shahram Rezapour, Sabri T. M. Thabet, Imed Kedim, Miguel Vivas-Cortez, Mehran Ghaderi. A computational method for investigating a quantum integrodifferential inclusion with simulations and heatmaps[J]. AIMS Mathematics, 2023, 8(11): 27241-27267. doi: 10.3934/math.20231394

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Abstract

We aim to investigate an integro-differential inclusion using a novel computational approach in this research. The use of quantum calculus, and consequently the creation of discrete space, allows the computer and computational algorithms to solve our desired problem. Furthermore, to guarantee the existence of the solution, we use the endpoint property based on fixed point methods, which is one of the most recent techniques in fixed point theory. The above will show the novelty of our work, because most researchers use classical fixed point techniques in continuous space. Moreover, the sensitivity of the parameters involved in controlling the existence of the solution can be recognized from the heatmaps. For a better understanding of the issue and validation of the results, we presented numerical algorithms, tables and some figures in our examples that are presented at the end of the work.

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