On a new definition of the fractional difference

Authors:
Henry L. Gray and Nien Fan Zhang

Journal:
Math. Comp. **50** (1988), 513-529

MSC:
Primary 39A12; Secondary 26A33, 39A10

DOI:
https://doi.org/10.1090/S0025-5718-1988-0929549-2

MathSciNet review:
929549

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Abstract | References | Similar Articles | Additional Information

Abstract: A new definition of the fractional difference is introduced. Many properties based on this definition are established including an extensive exponential law and the important Leibniz rule. The results are then applied to solving second-order linear difference equations.

**[1]**J. B. Diaz & T. J. Osler, "Differences of fractional order,"*Math. Comp.*, v. 28, 1974, pp. 185-201. MR**0346352 (49:11077)****[2]**C. W. J. Granger & R. Joyeux, "An introduction to long-memory time series models and fractional differencing,"*J. Time Ser. Anal.*, v. 1, 1980, pp. 15-29. MR**605572 (82d:62140)****[3]**J. R. M. Hosking, "Fractional differencing,"*Biometrika*, v. 68, 1981, pp. 165-176. MR**614953 (82k:62169)****[4]**G. L. Isaacs, "Exponential laws for fractional differences,"*Math. Comp.*, v. 35, 1980, pp. 933-936. MR**572866 (82e:39001)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0929549-2

Keywords:
Fractional difference,
backward difference operator,
Leibniz rule,
difference equation

Article copyright:
© Copyright 1988
American Mathematical Society