A comparative study on the behavior of Riemann-Liouville and Caputo fractional derivatives of some functions

Authors

  • Abdlgader M. Inbaig
  • Yasmina M. Bashon

DOI:

https://doi.org/10.37376/ljst.v14i2.7209

Keywords:

Fractional Calculus, Riemann-Liouville fractional derivative operator, Caputo fractional derivative operator

Abstract

This paper presents an overview of fractional order derivative operators. Particular attention is devoted to the Riemann-Liouville and Caputo fractional derivative operators. A comparative study of these two frameworks to show how they behave geometrically. The computation results of some elementary function derivatives of fractional order are shown in graphic form and tabular for this purpose.  The conclusion will include a few observations about derivatives of integer and fr Abdlgader M. Inbaig, Yasmina M. Bashon

actional order.

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References

Baleanu, D. a. (2019) 'On fractional operators and their classifications', Mathematics, 7(9), p. 830.

Campos, L. (1993) Fractional calculus of analytic and branched functions. Recent Advances in Fractional Calculus, Global Publishing Company.

Davis, P. J. (1972) Gamma function and related functions. Handbook of mathematical functions with formulas, graphs, and mathematical tables, 253-293.

De Oliveira, E. C. (2014) A review of definitions for fractional derivatives and integral. Mathematical Problems in Engineering. Garrappa, R. a. (2021) 'Variable-order fractional calculus: a change of perspective', Communications in Nonlinear Science and Numerical Simulation, 102, Art. No. 105904.

Herzallah, Mohamed A.E. (2014) 'Notes on some fractional calculus operators and their properties', J. Fract. Calc. Appl, 5(19), pp. 1-10.

Ishteva, M. (2005) Properties and applications of the Caputo fractional operator. Department of Mathematics, University of Karlsruhe, Karlsruhe, 5.

Labade, M. B. (2021) 'An Overview of Definitions of Riemann-Liouville's Fractional Derivative and Caputo's Fractional Derivative', International Journal of Science and Research (IJSR), 10(4), pp. 1210-1212.

Mainardi, F. a. (2013) Fractional calculus and special functions. Lecture Notes Math. Phys. Univ. Bologna: Bologna, Italy, pp. 1-64.

Miller, K. S. (1993) An introduction to the fractional calculus and fractional differential equations. Wiley.

Oldham, K. A. (1974) The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier

Vaidya, A. (2017) Finding the value of fractional 2pi: What is the effect of fractional derivatives and integrals on the properties of standard trigonometric functions?

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Published

2025-02-02

How to Cite

Inbaig, A. M. ., & Bashon, Y. M. . (2025). A comparative study on the behavior of Riemann-Liouville and Caputo fractional derivatives of some functions. Libyan Journal of Science &Amp;Technology, 14(2), 127–138. https://doi.org/10.37376/ljst.v14i2.7209

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Articles