Fractional calculus on time scales with Taylor’s theorem. (English) Zbl 1312.26059
Summary: We present a definition of the Riemann-Liouville fractional calculus for arbitrary time scales through the use of time scales power functions, unifying a number of theories including continuum, discrete and fractional calculus. Basic properties of the theory are introduced including integrability conditions and index laws. Special emphasis is given to extending Taylor’s theorem to incorporate our theory.
MSC:
| 26E70 | Real analysis on time scales or measure chains |
| 26A33 | Fractional derivatives and integrals |
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