A unified fractional action integral framework for memory-dependent circuit dynamics and Josephson junctions

Rami Ahmad El-Nabulsi; Waranont Anukool; Raja Valarmathi; Chinnasamy Thangaraj

doi:10.1016/j.jnlest.2026.100362

Journal of Electronic Science and Technology ›› 2026, Vol. 24 ›› Issue (2) :100362 DOI: 10.1016/j.jnlest.2026.100362

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A unified fractional action integral framework for memory-dependent circuit dynamics and Josephson junctions

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^a Center of Excellence in Quantum Technology, Chiang Mai University, Chiang Mai, 50200, Thailand

^b Quantum-Atom Optics Laboratory and Research Center for Quantum Technology, Chiang Mai University, Chiang Mai, 50200, Thailand

^c Department of Optical Networks, CESNET a.l.e., Prague, 16000, Czech Republic

^d Department of Physics and Materials Science, Chiang Mai University, 50200, Thailand

^e Department of Mathematics, Dayananda Sagar Academy of Technology and Management, Bengaluru, 560082, India

^f Department of Mathematics, Dayananda Sagar College of Engineering, Bengaluru, 560078, India

^* E-mail addresses: nabulsiahmadrami@yahoo.fr (R.A. El-Nabulsi),

w.anukool1@gmail.com (W. Anukool),

valarmathi.2142@gmail.com (R. Valarmathi),

ctrmath1@gmail.com (C. Thangaraj).

Rami Ahmad El-Nabulsia received his Ph.D. in particle physics, mathematical physics and modeling from Provence University, France, in 2000, following advanced studies in plasma physics and radiation astrophysics and a strong foundation in physics and applied mathematics in 1997. He earned his Ph.D. in particle physics, mathematical physics and modeling from Provence University, following advanced studies in plasma physics and astrophysics and a strong foundation in physics and applied mathematics. He is now a theoretical physicist and applied mathematician affiliated with the Center of Excellence in Quantum Technology and the Quantum-Atom Optics Laboratory at Chiang Mai University, Thailand, as well as CESNET, Department of Optical Networks, Prague. With extensive academic and research experience, he has contributed to pioneering projects across nonlinear quantum physics, geometrical physics, physics of the condensed matter and materials science, neurocomputing, superconductivity, nuclear engineering, chaos, cosmology, astrophysics, and space sciences, establishing new models and mathematical frameworks that deepen understanding of complex physical systems. As a prolific author with more than 400 peer-reviewed publications in leading international journals, Dr. El-Nabulsi's work bridges theoretical innovation with real-world applications. He has received numerous honors, including recognition among the Top 2% of scientists worldwide, Lifetime Achievement Award, Outstanding Researcher Award, Pioneer Research Award, Neurocomputing Innovator Excellence Award, Excellence in Innovator Award, Nanophotonic Research Award, Top Researcher Award, Quantum Research Leader Award, International Research Scientist Award, and Optical Networks Excellence in Innovation Award, and is a highly sought-after invited speaker at global scientific forums. He serves as a reviewer for more than 250 international journals, contributing significantly to the development of advanced physics and applied sciences.

Waranont Anukool received a Ph.D. in Physics from the University of Cambridge, UK, in 2003. He has 10-year research experience in the transport properties of superconductivity and Josephson integrated circuits before proceeding into the atomic, molecular, and optical (AMO) physics focusing on exploiting laser cooled atoms and atomic ensemble. His research group, the Quantum-atom Optics Laboratory, has been installed in 2010 and now comprises 7 laboratories ranging from quantum sensors and metrology to quantum simulation using neutral atoms and error suppression algorithm for Noisy Intermediate Scale Quantum Computing. At present, he is the leader of the Establishment Project of the Center of Excellence for Quantum Technology established and funded by Chiang Mai University in 2019.

Raja Valarmathi received her Ph.D. in mathematics from Vellore Institute of Technology, India, in 2023. She is currently working as an assistant professor at Dayananda Sagar Academy of Technology and Management, Bangalore. She has over six years of research experience in fractal analysis and fractional calculus. Her work focuses on fractal interpolation functions, dynamical systems, and chaos theory. She has published several papers in reputed international journals and collaborated with global researchers.

Chinnasamy Thangaraj received his Ph.D. in mathematics from Vellore Institute of Technology, India, in 2023. He is currently working as an assistant professor at Dayananda Sagar College of Engineering, Bangalore. He has over six years of research experience in fractal analysis and fixed-point theory. His work focuses on fractal dimension, dynamical systems, and chaos theory. He has published several papers in reputed international journals and collaborated with global researchers.

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Abstract

This study presents a unified framework for analyzing electric circuits and Josephson junctions using a fractional action integral that incorporates memory effects and nonlocal behavior. Unlike classical integer-order models, the method extends the action principle to fractional orders, leading to fractional Euler-Lagrange equations that better describe currents, voltages, and phase evolution. It is particularly effective for Josephson junctions, where tunneling currents and phase dynamics show long-term correlations and dissipation. By including fractional-order elements, the framework captures anomalous damping, power-law relaxation, and persistent memory effects in complex circuits. Using a dissipative fractional standard map, the study investigates chaos and the influence of memory on system stability. Numerical results reveal strong sensitivity to fractional parameters, including bifurcations and chaotic attractors. These findings link the classical circuit theory with fractional dynamics, offering new insights for superconducting electronics and the design of nonlinear systems.

Keywords

Electric circuits / Josephson junction / Fractional-order integral / Chaos

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Rami Ahmad El-Nabulsi, Waranont Anukool, Raja Valarmathi, Chinnasamy Thangaraj. A unified fractional action integral framework for memory-dependent circuit dynamics and Josephson junctions. Journal of Electronic Science and Technology, 2026, 24 (2) : 100362 DOI:10.1016/j.jnlest.2026.100362

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CRediT authorship contribution statement

Rami Ahmad El-Nabulsi: Writing–original draft, Methodology, Investigation, Formal analysis, Conceptualization, Supervision. Waranont Anukool: Validation, Resources, Conceptualization. Raja Valarmathi: Softwares, Writing–review & editing. Chinnasamy Thangaraj: Softwares, Writing–review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the Ministry of Education, Youth and Sport of the Czech Republic as a part of the Quantum Engineering and Nanotechnology project QUEENTEC, reg. nr. CZ.02.01.01/00/22 008/0004649, Chiang Mai University. The authors would like to thank the group of anonymous reviewers for useful comments and valuable suggestions.

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