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





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.


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Author Biographies

Cristina de Andrade Santos Reis, Universidade Estadual do Sudoeste da Bahia, Vitória da Conquista-BA, Brasil

Especialista em Matemática e Estatística pela Faculdade Cidade de Guanhaes (FACIG) e em Mídias na Educação pela Universidade Estadual do Sudoeste da Bahia (UESB). Professora da Universidade Estadual do Sudoeste da Bahia (UESB) e autora do livro Cálculo Diferencial e Integral pela DTCom. Atualmente tem interesse por Ciência de Dados, Business Intelligence, Linguagem R e Linguagem Python.

Rinaldo Vieira da Silva Junior, Universidade Federal de Alagoas, Arapiraca-AL, Brasil

Doutor em Matemática Aplicada pela Universidade Estadual de Campinas. Atualmente é professor Adjunto nível 3 da Universidade Federal de Alagoas. Tem experiência na área de Matemática, com ênfase em Geometria e Topologia, atuando principalmente nos seguintes temas: Geometria de Finsler, Equações diferenciais e Modelagem Matemática.


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How to Cite

Reis, C. de A. S., & Silva Junior, R. V. da. (2021). A new non-conformable derivative based on Tsallis’s q- exponential function. INTERMATHS, 2(2), 106-118. https://doi.org/10.22481/intermaths.v2i2.10101