Fractional Fourier transform in the framework of fractional calculus operators. (English) Zbl 1205.42010
In this paper connections of fractional Fourier transform with differential operators are established and an operator inverse to such a transform from left is constructed. Next, compositions of this transform with modified fractional integrals and derivatives are proved. Finally, an application of the fractional Fourier transform and the composition formulas to a solution of a Cauchy problem for partial diffusion-type differential equations of fractional order is obtained.
Reviewer: Som Prakash Goyal (Jaipur)
MSC:
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 26A33 | Fractional derivatives and integrals |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 44A10 | Laplace transform |
| 33E12 | Mittag-Leffler functions and generalizations |
Keywords:
Fourier and fractional Fourier transforms; diffusion-type fractional differential equation; Mittag-Leffler functionReferences:
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