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Fractional differential equations

Fractional differential equations,I. Podlubny

Fractional differential equations   (Citations: 1049)
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Published in 1999.
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    • ...Variety of models having positive linear behavior can be found in engineering, management sciences,economics,socialsciences,biology,medicine,etc.Mathematical fundamentals of the fractional calculus are given in the monographs [25]–[27], [29] and the fractional differential equations and their applications have been addressed in [20], [22], and [23]...

    Tadeusz Kaczorek. Positive Linear Systems Consisting of $n$ Subsystems With Different Fr...

    • ...[1], [4], [9], [11], [8], [19], [21] the survey paper [7] and references therein...

    Carlos Lizama. An operator theoretical approach to a class of fractional order differ...

    • ...d dspk (s) (t ¡ s)” ds, for 0 < ” < 1 (1.4) (see Podlubny [12])...
    • ...Fractional equations of various types have proved to be useful in representing dierent phenomena in optics (light propagation through random media), transport of charge carriers and also in economics (a survey of applications can be found in Podlubny [12])...

    Enzo Orsingheret al. Fractional pure birth processes

    • ... of fractional integration and fractional dierentiation [52], a physical interpretation for the initial conditions in terms of the Riemann-Liouville fractional derivatives of the unknown function has been suggested [27], the use of Caputo derivative in physical problems is perhaps more convenient since it allows using initial conditions expressed in terms of values of the unknown function and its integer-order derivatives [50]...
    • ...where @ =@jxj (we adopt here the notation introduced in [54]) is a partial (with respect to spatial variable) symmetric Riesz derivative, which is dened as a half-sum of the left- and right-sided Riemann-Liouville derivatives [50, 51]:...
    • ...Since the Caputo derivative of a constant is zero [2, 50], for the auxiliary functiony(x;t) dened by equation (40) we obtain a problem with zero initial and boundary conditions similar to (41){(42):...

    Igor Podlubnyet al. Matrix approach to discrete fractional calculus II: Partial fractional...

    • ...respectively. Note that for suciently smooth functions ’ for which ’(0) = 0 the left Caputo and Riemann-Liouville derivatives coincide ([12], Formula (2.165)), i.e...

    J. Kemppainenet al. Boundary Integral Solution of the Time-Fractional Diffusion Equation

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