926 resultados para Riemann-Liouville fractional derivative, Grunwald-Letnikov fractional derivative, Caputo fractional derivative, Riesz fractional derivative, fractional Laplacian, anomalous diffusion, fractional diffusion equation, fractional advection-dispersion equation
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Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.
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2000 Mathematics Subject Classification: 26A33, 42B20
Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations
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Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12
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Mathematics Subject Classification: 74D05, 26A33
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Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05
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Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10
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Mathematics Subject Classification: 33D60, 33E12, 26A33
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Mathematics Subject Classification: 26A33, 31B10
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Mathematics Subject Classification: 26A33, 33C60, 44A15
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Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.
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MSC 2010: 26A33, 33E12, 33C60, 35R11
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MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo
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MSC 2010: 35R11, 42A38, 26A33, 33E12
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In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.
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In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.