2014
DOI: 10.1142/s0218127414300237
|View full text |Cite
|
Sign up to set email alerts
|

Memfractance: A Mathematical Paradigm for Circuit Elements with Memory

Abstract: Memristor, the missing fourth passive circuit element predicted forty years ago by Chua was recognized as a nanoscale device in 2008 by researchers of a H. P. Laboratory. Recently the notion of memristive systems was extended to capacitive and inductive elements, namely, memcapacitor and meminductor whose properties depend on the state and history of the system. In this paper, we use fractional calculus to generalize and provide a mathematical paradigm for describing the behavior of such elements with memory. … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

1
87
0
3

Year Published

2015
2015
2023
2023

Publication Types

Select...
8
1

Relationship

1
8

Authors

Journals

citations
Cited by 101 publications
(91 citation statements)
references
References 20 publications
1
87
0
3
Order By: Relevance
“…Recently, fractional calculus is generalized and a mathematical paradigm is provided for describing the behavior of mem-elements with memory. Ohm's law is generalized and proved in case of fractional mem-element which is called memfractance [28].…”
Section: Fractional-order Elements Relationsmentioning
confidence: 99%
“…Recently, fractional calculus is generalized and a mathematical paradigm is provided for describing the behavior of mem-elements with memory. Ohm's law is generalized and proved in case of fractional mem-element which is called memfractance [28].…”
Section: Fractional-order Elements Relationsmentioning
confidence: 99%
“…Tenreiro Machado studied the generalization of the memristor in the perspective of the fractional-order systems [45]. In 2014, Abdelhouahad proposed the memfractor, which interpolates characteristics between the memristor and the memcapacitor, the meminductor or the second-order memristor [46].…”
Section: Introductionmentioning
confidence: 99%
“…The application of fractional calculus to analyzing the memristor is an emerging discipline of study in which few studies have been performed [43]- [46]. In the scientific fields of latest signal analysis, signal processing, and circuits and systems, there are many issues on non-linear, non-causal, non-Gaussian, non-stationary, non-minimum phase, non-white additive noise, non-integer-dimensional, and non-integer-order characteristics needed to be analyzed and processed.…”
Section: Introductionmentioning
confidence: 99%
“…In [9], we have generalised the definition of fractance (which was first introduced in 1983) and after that introduced the paradigm of memfractance which is fitted for circuit elements with memory such as memristor, meminductor, memcapacitor and second-order memristor. We have defined a new element called memfractor which possesses interpolated characteristics between those four circuit elements and proved a generalised Ohm's law.…”
Section: Introductionmentioning
confidence: 99%