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Dual conformable derivative: Definition, simple properties and perspectives for applications

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  • Rosa, Wanderson
  • Weberszpil, José

Abstract

In this communication, one shows that there exists in the literature a certain form of deformed derivative that can here be identified as the dual of conformable derivative. The conformable subtraction is defined and used here, together with the duality concept, as the basic definitions and starting points in order to obtain the connected dual operators. The q-exponential, in the context of generalized statistical mechanics, is the eigenfunction of this dual conformable derivative. The basic properties of the dual deformed-derivatives and also some perspective of applications and simple models are presented. The importance of this deformed derivative for position-dependent models is highlighted. An outlook of potential applications and developments is presented.

Suggested Citation

  • Rosa, Wanderson & Weberszpil, José, 2018. "Dual conformable derivative: Definition, simple properties and perspectives for applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 137-141.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:137-141
    DOI: 10.1016/j.chaos.2018.10.019
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    References listed on IDEAS

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    1. Naudts, Jan, 2004. "Generalized thermostatistics based on deformed exponential and logarithmic functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 32-40.
    2. Godinho, Cresus F.L. & Weberszpil, J. & Helayël-Neto, J.A., 2012. "Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 765-771.
    3. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.
    4. Balankin, Alexander S. & Bory-Reyes, Juan & Shapiro, Michael, 2016. "Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 345-359.
    5. Weberszpil, J. & Helayël-Neto, J.A., 2016. "Variational approach and deformed derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 217-227.
    6. Borges, Ernesto P., 2004. "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 95-101.
    7. Weberszpil, J. & Lazo, Matheus Jatkoske & Helayël-Neto, J.A., 2015. "On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 399-404.
    8. Costa Júnior, Manoel Pedro da & Khan, Ahmad Saeed & Sousa, Eliane Pinheiro de & Lima, Patrícia Verônica Pinheiro Sales, 2015. "53," Revista de Economia e Sociologia Rural (RESR), Sociedade Brasileira de Economia e Sociologia Rural, vol. 53(2), January.
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    Cited by:

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    3. Martynyuk, Anatoliy A. & Stamov, Gani Tr. & Stamova, Ivanka M., 2020. "Fractional-like Hukuhara derivatives in the theory of set-valued differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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