On pantograph \(\psi\)-Caputo integro-differential problems via upper and lower solutions
Authors
H. Bouzid
- Department of Mathematics, Faculty of Exact Science and Informatics, Hassiba Benbouali University of Chlef, Ouled Fares, Chlef 02000, Laboratory of Mathematics and Applications (LMA), Algeria.
A. Benali
- Department of Mathematics, Faculty of Exact Science and Informatics, Hassiba Benbouali University of Chlef, Ouled Fares, Chlef 02000, Laboratory of Mathematics and Applications (LMA), Algeria.
A. Salim
- Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria.
- Laboratory of Mathematics, Djillali Liabes University of Sidi-Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria.
I. Alraddadi
- Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia.
Abstract
In this study, we explore the existence of positive solutions for a class of fractional differential pantograph equations that incorporate the \(\psi\)-Caputo fractional derivative under specified initial conditions. By reformulating the problem as an equivalent Riemann-Liouville integral equation, we rigorously derive our principal results using the upper and lower solutions method. Lastly, we present an example to
demonstrate the validity of our results.
Share and Cite
ISRP Style
H. Bouzid, A. Benali, A. Salim, I. Alraddadi, On pantograph \(\psi\)-Caputo integro-differential problems via upper and lower solutions, Journal of Mathematics and Computer Science, 40 (2026), no. 4, 533--541
AMA Style
Bouzid H., Benali A., Salim A., Alraddadi I., On pantograph \(\psi\)-Caputo integro-differential problems via upper and lower solutions. J Math Comput SCI-JM. (2026); 40(4):533--541
Chicago/Turabian Style
Bouzid, H., Benali, A., Salim, A., Alraddadi, I.. "On pantograph \(\psi\)-Caputo integro-differential problems via upper and lower solutions." Journal of Mathematics and Computer Science, 40, no. 4 (2026): 533--541
Keywords
- Fractional differential pantograph equations
- \(\psi\)-fractional integral and derivative
- Arzelá-Ascoli theorem
- upper and lower solutions
MSC
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