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.
| Original language | English |
|---|---|
| Pages (from-to) | 27241-27267 |
| Number of pages | 27 |
| Journal | AIMS Mathematics |
| Volume | 8 |
| Issue number | 11 |
| DOIs | |
| State | Published - 2023 |
Bibliographical note
Publisher Copyright:© 2023 the Author(s), licensee AIMS Press.
Funding
This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1445). Pontificia Universidad Católica del Ecuador, Proyecto Título: “Algunos resultados Cualitativos sobre Ecuaciones diferenciales fraccionales y desigualdades integrales” Cod UIO2022. The authors express their gratitude dear unknown referees for their helpful suggestions which improved final version of this paper.
Keywords
- Pompieu-Hausdorff metric
- boundary value problem
- endpoint property
- fixed point theory
- fractional calculus
- integro-differential inclusion
- quantum calculus