On the generalized fractional derivatives and their Caputo modification
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Abstract
In this manuscript, we define the generalized fractional derivative on AC(gamma)(n) [a, b], the space of functions defined on [a, b] such that gamma(n-1) f is an element of AC [a, b], where gamma = x(1-rho) d/dx. We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo version.
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Keywords
Riemann-Liouville Fractional Derivatives, Caputo Fractional Derivatives, Hadamard Fractional Derivatives, Caputo-Hadamard Fractional Derivatives, Generalized Fractional Integral, Generalized Caputo Fractional Derivatives, generalized Caputo fractional derivatives, Fractional derivatives and integrals, Fractional ordinary differential equations, Caputo fractional derivatives, Hadamard fractional derivatives, Caputo-Hadamard fractional derivatives, generalized fractional integral, Riemann-Liouville fractional derivatives
Fields of Science
0101 mathematics, 01 natural sciences
Citation
Jarad, Fahd; Abdeljawad, Thabet; Baleanu, Dumitru (2017). "On the generalized fractional derivatives and their Caputo modification", JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, Vol. 10, No. 5, pp. 2607-2619.
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OpenCitations Citation Count
225
Volume
10
Issue
5
Start Page
2607
End Page
2619
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