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A Review on Integral Transforms of Fractional Integral and Derivative
International Academic Journal of Science and Engineering, 2022In this paper, we present a review of the integral transformations of fractional calculus, namely the Riemann-Liouville integral, the Riemann-Liouville derivative, and the Caputo derivative.
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Fractional derivatives, fractional integrals and electromagnetic theory
1999 International Conference on Computational Electromagnetics and its Applications. Proceedings (ICCEA'99) (IEEE Cat. No.99EX374), 2003Summary form only given. Fractional derivatives/integrals are mathematical operators involving differentiation/integration to arbitrary noninteger orders-orders that may be fractional or even complex. These operators, which possess interesting mathematical properties, have been studied in the field of fractional calculus.
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a -times integrated semigroups and fractional derivation
form, 2002The work is devoted to the \(\alpha\)-times integrated semigroups and functional calculus which is related to smooth distribution semigroups. The functional calculus for \(\alpha\)-times integrated semigroups is obtained by applying the fractional integration and derivation to the vector-valued Laplace transform.
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Asymptotic Evaluation of Integrals Involving a Fractional Derivative
SIAM Journal on Mathematical Analysis, 1974For the integral \[\int_\alpha ^\infty {e^{ - z(t - a )} I^{\lambda - 1} f(t)dt} \] an asymptotic expansion is obtained as $z \to \infty $. Here $\lambda $ is fixed, $0 < \lambda < 1, $, $I^{\lambda - 1} $ is the operator of fractional integration, and the expansion holds uniformly for $a \geqq 0$.
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Integration of Fractional Differential Equations without Fractional Derivatives
2021 9th International Conference on Systems and Control (ICSC), 2021Nezha Maamri, Jean-Claude Trigeassou
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Fractional derivatives: integral representations and generalized polynomials
2004Summary: 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 ...
DATTOLI G +3 more
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ON FRACTIONAL INTEGRALS AND DERIVATIVES
The Quarterly Journal of Mathematics, 1940openaire +2 more sources