Generalized Riemann-Liouville and Liouville-Caputo time fractional evolution equations associated to the number operator. (English) Zbl 1475.35382
Summary: By means of the Laplace transform, we give the solution of the generalized Riemann-Liouville and Liouville-Caputo time fractional evolution equations in infinite dimensions associated to the number operator. These solutions are given in terms of the Mittag-Leffler function and the convolution product.
MSC:
| 35R11 | Fractional partial differential equations |
| 34G10 | Linear differential equations in abstract spaces |
| 46E50 | Spaces of differentiable or holomorphic functions on infinite-dimensional spaces |
Keywords:
Liouville-Caputo time fractional evolution equation; Riemann-Liouville time fractional evolution equation; number operator; Mittag-Leffler type functions; nuclear space of holomorphic functionsReferences:
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