On a hybrid class of \(p\)-Laplacian boundary value problems with modified Mittag-Leffler kernel: application to nonlinear and mixed pharmacokinetic models

Volume 39, Issue 1, pp 50--70 https://dx.doi.org/10.22436/jmcs.039.01.04

Publication Date: March 06, 2025 Submission Date: August 31, 2024 Revision Date: October 21, 2024 Accteptance Date: December 16, 2024

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Authors

S. Ramasamy - Department of Mathematics, School of Sciences, Arts \(\&\) Media, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India. K. Velusamy - Department of Mathematics, School of Sciences, Arts \(\&\) Media, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India. D. Baleanu - Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon. M. A. Mani - Department of Mathematics, School of Arts, Sciences, Humanities and Education, SASTRA Deemed to be University, Thanjavur-613401, Tamil Nadu, India.

Abstract

This study investigates a class of hybrid fractional pantograph differential equations (HFPDEs) under the \(p\)-Laplacian operator \(LO\), employing the extended Mittag-Leffler kernel (\(MMLK\)). We establish the existence and uniqueness of solutions using Krasnoselskii and Banach fixed point theorems (FPTs), and further explore their stability properties. To bridge the gap between theory and practice, we develop a novel numerical method based on Lagrange's interpolation polynomial. The effectiveness of this method is demonstrated through its application to nonlinear and mixed pharmacokinetic models. A specific case is provided to confirm the validity of the theoretical results.

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Keywords

• Fractional-order
• existence and uniqueness
• stability
• FPTs
• \(MMLK\) fractional derivative

MSC

•  26A33
•  34A08
•  34D20

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