An algorithm for the numerical solution of differential equations of fractional order.
Monotonicity results for a compound quadrature method for finite-part integrals.
Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations
Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10 We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral...
Asymptotic behaviour of fixed-order error constants of modified quadrature formulae for Cauchy principal value integrals.
Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue
Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15 The popular elastic law of Fung that describes the non-linear stress- strain behavior of soft biological tissues is extended into a viscoelastic material model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a three-dimensional constitutive model that is suitable for general analysis. The model is derived in a configuration that differs from the...
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