Conformable fractional derivatives and applications to Newtonian dynamic and cooling body law
Keywords:Fractional derivatives, Nápoles' fractional derivative, free fall of bodies, cooling bodies
This article presents a rigorous review of the conformable fractional derivative given by J. E. Napoles in , studying its classical properties, as a differential operator. Likewise, applications are given to Physics, specifically to the free fall of bodies and Newton’s law of cooling.
Abdeljawad T, On Conformable Fractional Calculus. J. of Computational and Applied Mathematics. 2015M; 279:57-66.
Atangana A. Derivative with a New Parameter: Theory, Methods and Applications. London: Academic Press; 2016.
Atangana A, Secer A. A note on fractional order derivatives and table of fractional derivatives of some special functions. Abstr. Appl. Anal. 2013; 2013(1):1-7.
Atangana A, Kilicman A. A novel integral operator transform and its application to some FODE and FPDE with some kind of singularities. Math. Probl. Eng. 2013; 2013(1):1-7.
Hernández Hernández JE, Vivas-Cortez M. Hermite-Hadamard inequalities type for Raina’s fractional integral operator using n-convex functions. Revista Matemática: Teoría y Aplicaciones. 2019; 26(1):1-19.
Hernández Hernández J E, Vivas-Cortez M. On a Hardy’s inequality for a fractional integral operator. Annals of the University of Craiova, Math. and Computer Science Series 2018; 45(2):232-242.
Jackson FH. On q-functions and a certain difference operator. Trans. R. Soc. Edinb. 1908; 46:253-281.
Kanno R. Representation of random walk in fractal space-time. Phys. A. 1998; 248:165-175.
Katz VJ. Ideas of calculus in Islam and India. Math. Mag. 1995; 68(3):163-174.
Khalil R, Al-Horani M, Yousef A. Sababheh M. A new definition of fractional derivative. J. of Computational and Applied Math. 2014; 264:65-70.
Guzmán PM, Langton G, Lugo-Motta L, Medina J, N´apoles-Vald´es JE. A new definition of a fractional derivative of local type. J. Math. Anal. 2018; 9:88-96.
Riemman JL. Versuch einer allgemeinen Auffassung der Integration und Differentiation. In: Weber H. Bernhard Riemann’s gesammelte mathematische Werke und wissenschaftlicher Nachlass. Dover: Dover Publications; 1953. p. 353.
Vivas-Cortez M, Velasco J, Hernández Hernández JE. Certain new results on the Khalil conformable fractional derivative. Matua, Revista de la Universidad del Atlántico 2020; 7(1):1-8.
Vivas-Cortez M, Kashuri A, Hernández Hernández JE. Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized Convex Functions. Symmetry 2020; 12:1-17.
Vivas-Cortez M, Fleitas A, Guzman PM, Nápoles JE, Rosales JJ. Newton’s Law of cooling with generalized conformable derivatives. symetruy. 2021; 13(6)- 1093.
Vivas-Cortez M, Nápoles-Valdés J, Hernández Hernández JE, Velasco J, Larreal O. On Non Conformable Fractional Laplace Transform. Appl. Math. Inf. Sci. 2021; 15(4):403-409.
Umarov S, Steinberg S. Variable order differential equations with piecewise constant order-function and diffusion with changing modes. Z. Anal. Anwend. 2009; 28(4):431-450.
How to Cite
Copyright (c) 2022 Selecciones Matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.