A new non-conformable derivative based on Tsallis’s q- exponential function

• Main Author: Reis, Cristina de Andrade Santos
• Publication Date: 2021
• Other Authors: Silva Junior, Rinaldo Vieira da
• Format: Article
• Language: eng
• Source: Revista Intermaths
• Download full: https://periodicos2.uesb.br/intermaths/article/view/10101
• topic: Cálculo Fracionário; Derivada não compatível; Função q-exponencial; Fractional calculus; Non-conformable derivative; q-exponential function

In this paper, a new derivative of local type is proposed and some basic properties are studied. This new derivative satisfies some properties of integer-order calculus, e.g. linearity, product rule, quotient rule and the chain rule. Because Tsallis' generalized exponential function, we can extend some of the classical results, namely: Rolle's theorem, the mean-value theorem. We present the corresponding Q-integral from which new results emerge. Specifically, we generalize the inversion property of the fundamental theorem of calculus and prove a theorem associated with the classical integration by parts. Finally, we present an application involving linear differential equations by means of Q derivative.