Generalized special functions in the description of fractional diffusive equations
Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form...
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| Format: | Article |
| Language: | English |
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Sciendo
2019-01-01
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| Series: | Communications in Applied and Industrial Mathematics |
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| Online Access: | https://doi.org/10.1515/caim-2019-0010 |
| Summary: | Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form to d'Alembert and Fourier equations. We also show that the solutions of the generalized equations discussed here can be expressed in terms of Hermite-based functions. |
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| ISSN: | 2038-0909 |