Cauchy and Nonlocal Multi-Point Problems for Distributed Order Pseudo-Differential Equations, Part One

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Time-fractional Diffusion of Distributed Order (2007, methodology): “In section 4 we illustrate our method to get the fundamental solutions from their Fourier-Laplace transforms, following the strategy of carrying out at first the Fourier inversion and then the Laplace inversion.”
General Fractional Calculus, Evolution Equations, and Renewal Processes (2011, background): “where ρ is a Borel measure on [0, 1]; see [1, 6, 11, 14, 15, 16, 17, 21, 28].”
Numerical analysis for distributed-order differential equations (2009, background): “(1) We draw particular attention to the papers by [2, 3], [4, 5, 6, 7, 8], [19], [26], [25], and the paper by [1] which show the range of potential applications Gesellschaft für Numerische Simulation mbH, Am Gaußberg 2, 38114 Braunschweig, Germany Mathematics Department, University of Chester, CH1 4”
Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation (2011, unknown): “Differential equations of the distributed order and some of their applications were considered e.g. in [15] [26] [38].”
Distributed order calculus and equations of ultraslow diffusion (2007, unknown): “Umarov and Gorenflo [ 39 ] applied to equations (1.2) Dubinskij’s theory [8] of analytic pseudo-differential operators.”