Generic analytical models of memelement and inverse memelement with time-dependent memory effects

Abstract

Purpose
The purpose of this paper is to originally present the generic analytical models of memelement and inverse memelement with time-dependent memory effect.

Design/methodology/approach
The variable order forward Grünwald–Letnikov fractional derivative and the memristor and inverse memristor models proposed by Fouda et al. have been adopted as the basis. Both analytical and numerical studies have been conducted. The applications to the candidate practical memristor and inverse memelements have also been presented.

Findings
The generic analytical models of memelement and inverse memelement with time-dependent memory effect, the simplified ones for DC and AC signal-based analyses and the equations of crucial parameters have been derived. Besides the well-known opposite relationships with frequency, the Lissajous patterns of memelement and inverse memelement also use the opposite relationships with the time. The proposed models can be well applied to the practical elements.

Originality/value
To the best of the authors’ knowledge, for the first time, the models’ memelement and inverse memelement with time-dependent memory effect have been presented. A new contrast between these elements has been discovered. The resulting models are applicable to the practical elements.

Keywords: Inverse memelement, Memelement, Time-dependent memory effect, Variable order Grünwald–Letnikov fractional derivative

รศ. ดร.รวิศวร์ บานชื่น – Assoc. Prof. Dr. Rawid Banchuin. 2568 (2025). Generic analytical models of memelement and inverse memelement with time-dependent memory effects. บทความ (Paper). ปริญญาโท (Master’s Degree). บัณฑิตวิทยาลัย (Graduate School). วิทยาศาสตรมหาบัณฑิต สาขาวิชาเทคโนโลยีสารสนเทศ – Master of Science Program in Information Technology. วท.ม. (เทคโนโลยีสารสนเทศ) – M.Sc. (Information Technology). Bangkok: Siam University