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On the boundedness of the solution set for the ψ-Caputo fractional pantograph equation with a measure of non-compactness via simulation analysis.
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- Author(s): George, Reny; Al-shammari, Fahad; Ghaderi, Mehran; Rezapour, Shahram
- Source:
AIMS Mathematics (2473-6988); 2023, Vol. 8 Issue 9, p20125-20142, 18p- Subject Terms:
- Source:
- Additional Information
- Abstract: A large number of physical phenomena can be described and modeled by differential equations. One of these famous models is related to the pantograph, which has been investigated in the history of mathematics and physics with different approaches. Optimizing the parameters involved in the pantograph is very important due to the task of converting the type of electric current in the relevant circuit. For this reason, it is very important to use fractional operators in its modeling. In this work, we will investigate the existence of the solution for the fractional pantograph equation by using a new ψ-Caputo operator. The novelty of this work, in addition to the ψ-Caputo fractional operator, is the use of topological degree theory and numerical results from simulations. Techniques in fixed point theory and the use of inequalities will also help to prove the main results. Finally, we provide two examples with some graphical and numerical simulations to make our results more objective. Our data indicate that the boundedness of the solution set for the desired problem depends on the choice of the ψ(1) function. [ABSTRACT FROM AUTHOR]
- Abstract: Copyright of AIMS Mathematics (2473-6988) is the property of American Institute of Mathematical Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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