Stability of conformable linear differential systems: a behavioural framework with applications in fractional‐order control

Comparative analyses of electrical circuits with conventional and revisited definitions of circuit elements: a fractional conformable calculus approach

“…where l denotes the order of such derivative and 0 < l < 1. Noted that the definition of fractional conformable derivative as given by equation ( 1) is different from that adopted by Mayo-Maldonado et al (see Definition 1 in Mayo-Maldonado et al, 2020).…”

“…The fractional conformable derivative of g ( u ) ( D λ [ g ( u )]) which is a local fractional derivative, can be mathematically defined as (Khalil et al , 2014): where λ denotes the order of such derivative and 0 < λ < 1. Noted that the definition of fractional conformable derivative as given by equation (1) is different from that adopted by Mayo-Maldonado et al (see Definition 1 in Mayo-Maldonado et al , 2020).…”

“…The fractional derivatives, which are the extension of the conventional derivative, have been widely used in the analyses of electrical circuits whose orders can be arbitrary real values. Among various fractional derivatives, the fractional conformable derivative (Khalil et al , 2014) which is a local operator adopted in many previous works (Martinez et al , 2018; Piotrowska and Rogowski, 2019; Piotrowska, 2019; Gómez-Aguilar, 2018; Mayo-Maldonado et al , 2020; Carreño et al , 2019), has been found to be of our interest due to its consistency with conventional derivative and maximum accuracy in real world circuit modelling (Carreño et al , 2019). Such consistency does not exist in nonlocal fractional derivatives which in turn are also often cited (Guía et al , 2013; Francisco et al , 2014; Shah et al , 2014; Gómez et al , 2013; Ayoub et al , 2006; Atangana and Alkahtani, 2015; Gómez-Aguilar et al , 2017; Alsaedi et al , 2015; Gómez-Aguilar et al , 2016).…”

An Economic Model for OECD Economies with Truncated M-Derivatives: Exact Solutions and Simulations

“…Many fractional derivatives and integrals have been introduced in the literature, and one of the most popular differential operators in the last years has been the conformable derivative, which maintains certain properties that resemble those from integer-order calculus. Among the properties which are common to traditional calculus, we can quote the properties on the derivative of products and quotients of two functions, the chain rule, the formula for integration by parts, the Taylor series expansions, and the Laplace transform of some functions [17,18]. In fact, the study of economic equilibrium models are among the most interesting applications of the conformal derivative [19].…”

Novel Investigation of Multivariable Conformable Calculus for Modeling Scientific Phenomena

“…us, researchers have paid more attention to conformable derivative and other related local derivatives in modeling scientific phenomena. While there are some recent studies concerning the mathematical analysis of conformable calculus such as the multivariable conformable calculus [15] that was introduced in 2018, the behavior of conformable derivatives of functions in arbitrary Banach spaces [24] that was investigated in 2021, the differential geometry of curves [25] that was investigated in 2019 in the senses of conformable derivatives and integrals, and the behavioral framework for the conformable linear differential systems' stability [26] that was carefully studied in 2020 to utilize the importance of CoV in modeling scenarios of control theory and power electronics, our results in this work provide a comprehensive investigation of α-derivative of a function of SVs and all related properties, the CoV of CR for functions of SVs, and the CoV of IF m involving many numerical examples to validate our obtained results. According to the best of our knowledge, our original investigation in this article provides an essential mathematical analysis tool for researchers working on modeling phenomena in physics and engineering in the sense of conformable calculus because all theorems and properties in this work will be needed in such modeling scenarios.…”