A theoretical improvement of the Riemann-Liouville and Caputo fractional derivatives
Keywords:
Riemann-Liouville fractional derivative, Caputo fractional derivative, Laplace transform
Abstract
In this paper we propose new fractional derivatives which, from the theoretical viewpoint, improve the Riemann-Liouville and Caputo fractional derivatives. Furthermore, some useful properties of the new fractional derivatives are presented.
References
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Podlubny, Igor. Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation. Fract. Calc. App. Anal. 5 (2002), 367–386.
Polat, Refet. Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. Journal of Science and Technology 12 (2019),
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Rahimy, Mehdi. Applications of Fractional Differential Equations. Applied Mathematical Sciences 4(50) (2010), 2454–2455.
Romero, Luis Guillermo; Luque, Luciano L.; Dorrego, Gustavo Abel and Cerutti, Rubén A.; On the k-Riemann-Liouville Fractional Derivative. Int. J. Contemp. Math. Sciences 8(1) (2013), 41–42.
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C., Anselmi; P., Desantis and A., Scipioni. Nanoscale echanical and dynamical properties of DNA single molecules. Biophys Chem. 113 (2005), 209–221.
Blaszczyk, Tomasz. A Numerical Solution of a Fractional Oscillator Equation in a non-Resisting Medium with Natural Boundary Conditions. Romanian Reports in Physics 67(2) (2015), 350–351.
S., Coyal and Perkins C., Perkins N.. Looping mechanics of rods and DNA with non-homogeneous and discontinuous stiffness. Int. J. Non-Linear Mech. 43(10) (2008), 1121–1128.
A., Gorosko O. and K., Hedrih (Stevanovic). Analiticka dinamika (mehanika) diskretnih naslednih sistema. (Analytical Dynamics (Mechanics) of Discrete Hereditary Systems). Monograph, p. 426, YU ISBN 86-7181-054-2,2001.
A., Gorosko O. and K., Hedrih (Stevanovic). The construction of the Lagrange Mechanics of the discrete hereditary systems. Facta Universitatis, Series: Mechanics, Automatic Control and Robotics 6(1) (2007), 175–176.
Herzallah, Mohamed A. E.. Notes on Some Fractional Calculus Operators and their properties. Journal of Fractional Calculus and Applications, 5(19), 1–2.
A., Hedrih. Mechanical models of the double DNA. International Journal of Medical Engineering and Informatics 3(4) (2011), 394–410.
K., Hedrih (Stevanovic). Dynamics of coupled systems. Nonlinear Analysis: Hybrid Systems 2 (2008), 310–334.
Katugampola, Udita N.. A New Approach to Generalized Fractional Derivatives. Bulletin of Mathematical Analysis and Applications 6 (2014), 1–6.
Kilbas, Anatoly A.; Srivastava, Hari M. and Trujillo, Juan J.. Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies 204 (2006), 125–126.
Lazarevi, Mihailo et.al.. Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, Published by WSEAS Press (2014).
Liang, Song; Wu, Ranchao and Chen, Liping. Laplace Transform of Fractional Order Differential Equations. Electronic Journal of Differential Equations 2015(139) (2015), 1–3.
Medina, Gustavo D.; Ojeda, Nelson R.; Pereira, José H. and Romero,Luis G.. Fractional Laplace Transform and Fractional Calculus. International Mathematical Forum 12(20) (2017), 991–997.
Podlubny, Igor. Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation. Fract. Calc. App. Anal. 5 (2002), 367–386.
Polat, Refet. Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. Journal of Science and Technology 12 (2019),
258–259.
Rahimy, Mehdi. Applications of Fractional Differential Equations. Applied Mathematical Sciences 4(50) (2010), 2454–2455.
Romero, Luis Guillermo; Luque, Luciano L.; Dorrego, Gustavo Abel and Cerutti, Rubén A.; On the k-Riemann-Liouville Fractional Derivative. Int. J. Contemp. Math. Sciences 8(1) (2013), 41–42.
Singh, Dimple. Integral Transform of Fractional Derivatives. International Journal of Recent Research Aspects bf 4 (2017), 74–75.
Thaiprayoon, Chatthai; Ntouyas, Sotiris K. and Tariboon, Jessada. On the nonlocal Katugampola fractional integral conditions for fractional Langevin equation. Advances in Difference Equations (2015), DOI 10.1186/s13662-015-0712-3.
Published
2020-12-27
How to Cite
MBoro NChama, G. A. (2020). A theoretical improvement of the Riemann-Liouville and Caputo fractional derivatives. Divulgaciones Matemáticas, 21(1-2), 33-41. Retrieved from https://produccioncientificaluz.org/index.php/divulgaciones/article/view/36602
Section
Research papers
