• Shashikant Waghule K.T.H.M. College, Nashik-422002, SPPU
  • Dr. Dinkar Patil K.T.H.M. College, Nashik-422002, SPPU
  • Dr. Amjad Shaikh K.T.H.M. College, Nashik-422002, SPPU


Riemann-Liouville Fractional Derivative, Caputo Fractional Derivative, Caputo-Fabrizio Derivative, Atangana-Baleanu Derivative, Variable Order Derivative, Fractional Difference Operator


In past three decades, the research on Fractional Calculus helped to solve real-life problems. Many Fractional Differential Operators are developed to solve different types of problems. In this article we reviewed the literature about different fractional differential operators like Riemann-Liouville Fractional Derivative, Caputo Fractional Derivative, Caputo Fabrizio Fractional Derivative, Atangana-Baleanu Fractional Derivative, Variable Order Fractional Derivative, Fractional Difference Operator, Modified Fractional Difference Operator and their applications.


I. A. A. Alikhanov, A new difference scheme for the time fractional diffusion equation, J. Comput. Phys., 280 (2015), 424-438.

II. A. Atangana and D. Baleanu, New fractional derivative without nonlocal and nonsingular kernel: theory and application to heat transfer model, Therm. Sci. 20 (2016), 763–769.

III. R. L. Bagley, and P. J. Torvik, On the fractional calculus model of viscoelastic behavior, Journal of Rheology, 30 (1986), 133-155.

IV. P. Baliarsingh, On a fractional difference operator, Alexandria Engineering Journal (2016) 55, 1811–1816

V. M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl. 1 (2015), 73–85.

VI. G. W. Leibniz. “Letter from Hanover, Germany to G.F.A. L’Hospital, September 30, 1695”, Leibniz Mathematische Schriften. Olms-Verlag, Hildesheim, Germany, (1962). 301-302

VII. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, (1999).

VIII. B. Ross, A brief history and exposition of the fundamental theory of fractional calculus, Lect. Notes Math. 457, (1975), 1–36.

IX. Stefan G. Samko & Bertram Ross (1993) Integration and differentiation to a variable fractional order, Integral Transforms and Special Functions, 1:4, 277-300

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How to Cite

Shashikant Waghule, Dr. Dinkar Patil, & Dr. Amjad Shaikh. (2023). A REVIEW ON FRACTIONAL DIFFERENTIAL OPERATORS AND THEIR APPLICATIONS. International Education and Research Journal (IERJ), 9(5). Retrieved from https://ierj.in/journal/index.php/ierj/article/view/2700