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Fractional Calculus

Published online by Cambridge University Press:  03 November 2016

W. Fabian
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Extract

We continue here our work on fractional integration and differentiation of functions of a real variable which we began in a previous paper. All quantities in the present paper are real.

We define a λth integral, or a (−λ)th differential coefficient, of f(x) over an interval (a, x)by

where D stands for and γ is the least integer greater than or equal to zero such that λ + γ>0, f(x) is bounded on the path of integration, and is continuous on this path except possibly for a finite number of ordinary discontinuities.

Type
Research Article
Information
The Mathematical Gazette , Volume 21 , Issue 244 , July 1937 , pp. 216 - 219
Copyright
Copyright © Mathematical Association 1937

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References

Page no 216 note * Fabian, , Math. Gazette, vol. 20 (1936), pp. 88–92. In our other previous papers on the Fractional Calculus the complex variable was used.CrossRefGoogle Scholar

Page no 218 note * Fabian, , Phil. Mag. vol. 20 (1935), pp. 781–789.CrossRefGoogle Scholar

Page no 218 note † Fabian, , Math. Gazette, vol. 20 (1936), pp. 88–92.CrossRefGoogle Scholar

Page no 219 note * Fabian, , Math. Gazette, vol. 20 (1936), pp. 88–92.CrossRefGoogle Scholar