Fractional derivatives: Integral representations and generalized polynomials
Fractional derivatives: Integral representations and generalized polynomials
Summary: We show that the use of functions associated with generalized forms of Hermite polynomials provide a natural tool for the solution of partial differential equations involving fractional derivatives. Within such a context we clarify the meaning of exponential operators with fractional derivatives and discuss alternative definitions based on integral transforms.
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Hermite polynomials, Kampé de Fériet polynomials, fractional derivatives, Fractional derivatives and integrals, fractional power differential operators, Integral transforms of special functions, Miscellaneous topics in partial differential equations
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Hermite polynomials, Kampé de Fériet polynomials, fractional derivatives, Fractional derivatives and integrals, fractional power differential operators, Integral transforms of special functions, Miscellaneous topics in partial differential equations
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