Research Article

THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION

Volume: 38 Number: 2 June 1, 2021
  • Juan E. Nápoles Valdes
  • Paulo M. Guzmán
  • Luciano M. Lugo
  • Artion Kashurı

THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION

Abstract

In this paper, we present a general definition of a generalized derivative of local type using the well known Mittag-Leffler function. Some methodological remarks on the local fractional derivatives are also presented.

Keywords

References

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  2. [2] Agarwal, R. P., Benchohra, M. and Hamani, S. A., (2010) Survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. 109, 973–1033.
  3. [3] Bonilla, B., Rivero, M. and Trujillo, J. J., (2007) On systems of linear fractional differential equations with constant coefficients, Appl. Math. Comput. 187, 68–78.
  4. [4] Boyce,W. E. and DiPrima, R. C., (1977) Elementary Diflerential Equations, John Wiley and Sons, New York.
  5. [5] Diethelm, K., (2010) The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type (Springer Science and Business Media).
  6. [6] Deshpande, A. S., Daftardar-Gejji, V. and Vellaisamy, P., (2010) Analysis of intersections of trajectories of systems of linear fractional differential equations, Chaos 29, 013113; doi: 10.1063/1.5052067.
  7. [7] Diethelm, K., and Ford, N., (2012) Volterra integral equations and fractional calculus: Do neighboring solutions intersect?, J. Integral Equ. Appl. 24, 25–37.
  8. [8] Guzmán, P. M., Langton, G., Lugo, L. M., Medina, J. and Nápoles Valdés, J. E., (2018) A new definition of a fractional derivative of local type. J. Math. Anal., 9:2, 88-98.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Juan E. Nápoles Valdes This is me
0000-0003-2470-1090
Argentina

Paulo M. Guzmán This is me
0000-0002-7490-5668
Argentina

Luciano M. Lugo This is me
0000-0001-9351-2547
Argentina

Artion Kashurı This is me
0000-0003-0115-3079
Albania

Publication Date

June 1, 2021

Submission Date

February 5, 2020

Acceptance Date

April 4, 2020

Published in Issue

Year 2020 Volume: 38 Number: 2

APA
Valdes, J. E. N., Guzmán, P. M., Lugo, L. M., & Kashurı, A. (2021). THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION. Sigma Journal of Engineering and Natural Sciences, 38(2), 1007-1017. https://izlik.org/JA73PN29PL
AMA
1.Valdes JEN, Guzmán PM, Lugo LM, Kashurı A. THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION. SIGMA. 2021;38(2):1007-1017. https://izlik.org/JA73PN29PL
Chicago
Valdes, Juan E. Nápoles, Paulo M. Guzmán, Luciano M. Lugo, and Artion Kashurı. 2021. “THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION”. Sigma Journal of Engineering and Natural Sciences 38 (2): 1007-17. https://izlik.org/JA73PN29PL.
EndNote
Valdes JEN, Guzmán PM, Lugo LM, Kashurı A (June 1, 2021) THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION. Sigma Journal of Engineering and Natural Sciences 38 2 1007–1017.
IEEE
[1]J. E. N. Valdes, P. M. Guzmán, L. M. Lugo, and A. Kashurı, “THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION”, SIGMA, vol. 38, no. 2, pp. 1007–1017, June 2021, [Online]. Available: https://izlik.org/JA73PN29PL
ISNAD
Valdes, Juan E. Nápoles - Guzmán, Paulo M. - Lugo, Luciano M. - Kashurı, Artion. “THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION”. Sigma Journal of Engineering and Natural Sciences 38/2 (June 1, 2021): 1007-1017. https://izlik.org/JA73PN29PL.
JAMA
1.Valdes JEN, Guzmán PM, Lugo LM, Kashurı A. THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION. SIGMA. 2021;38:1007–1017.
MLA
Valdes, Juan E. Nápoles, et al. “THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION”. Sigma Journal of Engineering and Natural Sciences, vol. 38, no. 2, June 2021, pp. 1007-1, https://izlik.org/JA73PN29PL.
Vancouver
1.Juan E. Nápoles Valdes, Paulo M. Guzmán, Luciano M. Lugo, Artion Kashurı. THE LOCAL GENERALIZED DERIVATIVE AND MITTAG-LEFFLER FUNCTION. SIGMA [Internet]. 2021 Jun. 1;38(2):1007-1. Available from: https://izlik.org/JA73PN29PL

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/