Khalil Conformable fractional derivative and its applications to population growth and body coolingin models

Authors

  • Jaime David Villacís Lascano Instituto de Posgrado, Universidad Técnica de Manabí, Manabí, Ecuador.
  • Miguel José Vivas-Cortez Escuela de Ciencias Matemáticas y Física, Facultad de Ciencias Naturales, Pontificia Universidad Católica del Ecuador, Quito, Ecuador.

DOI:

https://doi.org/10.17268/sel.mat.2022.01.04

Keywords:

Fractional derivatives, Khalil fractional derivative, fractional differential equations

Abstract

The objective of this article is to develop some results on conformable fractional derivatives, specifically the one known as Khalil’s conformable fractional derivative. Its origin, properties, comparisons with other fractional derivatives and some applications on population grow and Newton law of cooling models are studied.

References

Anastassiou GA. Fractional Differentiation Inequalities. New York: Springer; 2009.

Atangana A. Derivative with a New Parameter: Theory, Methods and Applications. London: Academic Press; 2016.

Bragdy M. On the Theory and Applications of Fractional Differential Equations[Doctoral Thesis]. Algeria: Universit´e Larbi Ben M’hidi d’Oum-El-Bougadi; 2013.

Diethelm K. The Analysis of Fractional Differentiasl Equations. New York: Springer; 2010.

Hernández Hernández J E, 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 JE, Vivas-Cortez M. On a Hardy’s inequality for a fractional integral operator. Annals of the University of Craiova, Mathematics and Computer Science Series 2018; 45(2):232-242.

Ishteva MK. Properties and Applications of Caputo Fractional Operator[Master Thesis]. Bulgaria: Universität Karlsruge; 2005.

Khalil R, Al-Horani M, Yousef A, Sababheh M. A new definition of fractional derivative. Journal of Computational and Applied Mathematics 2014; 264:65-70.

Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations. North Holland Mathematics Studies. Amsterdam: Elsevier; 2006.

Leibniz GW. Letter from Hannover to G. F. A. L’Hˆopital. Olms Verlag 1849, 2(1):301-302.

Nápoles JE, Guzmán PM, Lugo L , Kashuri A. The local non conformable derivative and Mittag Leffler function. Sigma J. Eng. & Nat. Sci. 2020; 38(2):1007-1017.

Riemann B. Versuch einer allgemeinen Auffassung der Integration und Differentiation, 1847. In: Weber H (ed) Bernhard Riemann’s gesammelte mathematische Werke und wissenschaftlicher Nachlass, Dover Publications; 1876.

Riesz M, L’integrale de Riemann-Liouville et le probleme de Cauchy. Acta Mathematica, 1949, 81(1):1-20.

Ross B, The development of fractional calculus 1695 to 1900. Historia Math. 1977, 4(1): 75-89.

Samko SG, Kilbas AA, Marichev OI, Fractional Integrals and Derivatives. Amsterdam: Gordon and Breachs Science Publishers; 1993.

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, Nápoles J E, Hernández Hernández J E, Velasco J, Larreal O. On Non Conformable Fractional Laplace Transform. Appl. Math. Inf. Sci. 2021; 15(4):403-409.

Weyl H. Bemerkungen zum Begriff des Differential quotienten gebrochener Ordnung. Vierteljahresschrift der Naturforsch. Ges. Zurich 1917; 62(296):10-27.

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Published

2022-07-27

How to Cite

Villacís Lascano, J. D., & Vivas-Cortez, M. J. (2022). Khalil Conformable fractional derivative and its applications to population growth and body coolingin models. Selecciones Matemáticas, 9(01), 44 - 52. https://doi.org/10.17268/sel.mat.2022.01.04