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Exact Solution of Linear Fractional Distributed Order Systems Chapter | 4  131


             Gao, G.H., Sun, Z.Z., 2016. Two unconditionally stable and convergent difference schemes with
                the extrapolation method for the one-dimensional distributed-order differential equations.
                Numer. Methods Partial Different. Eq. 32 (2), 591 615.
             Gao, G.H., Sun, H.W., Sun, Z.Z., 2015. Some high-order difference schemes for the distributed-
                order differential equations. J. Comput. Phys. 298, 337 359.
             Garra, R., Giusti, A., Mainardi, F., Pagnini, G., 2014. Fractional relaxation with time-varying
                coefficient. Fract. Calculus Appl. Anal. 17 (2), 424 439.
             Garrappa, R., Maione, G., Popolizio, M., 2014. Time-domain simulation for fractional relaxation
                of havriliak-negami type, in: Fractional Differentiation and Its Applications (ICFDA), 2014
                International Conference on, IEEE, pp. 1 6.
             Geller, M., Ng, E.W., 1969. A table of integrals of the exponential integral. J. Res. Natl Bureau
                Standards 71, 1 20.
             Gorenflo, R., Luchko, Y., Stojanovic, M., 2013. Fundamental solution of a distributed order
                time-fractional diffusion-wave equation as probability density. Fract. Calculus Appl. Anal.
                16 (2), 297 316.
             Hu, X., Liu, F., Turner, I., Anh, V., 2016. An implicit numerical method of a new time
                distributed-order and two-sided space-fractional advection-dispersion equation. Num. Alg.
                72 (2), 393 407.
             Jakovljevic, B.B., Rapaic, M.R., Jelicic, Z.D., Sekara, T.B., 2014. Optimization of distributed
                order fractional pid controller under constraints on robustness and sensitivity to measure-
                ment noise, in: Fractional Differentiation and Its Applications (ICFDA), International
                Conference on, IEEE, pp. 1 6.
             Jiao, Z., Chen, Y., Podlubny, I., 2012. Distributed-order dynamic systems: stability, simulation,
                applications and perspectives. springerbriefs in electrical and computer engineering/springer-
                briefs in control, automation and robotics.
             Jin, B., Lazarov, R., Zhou, Z., 2016. A petrov galerkin finite element method for fractional
                convection-diffusion equations. SIAM J. Numer. Anal. 54 (1), 481 503.
             Kochubei, A.N., 2009. Distributed order derivatives and relaxation patterns. J. Phys. A: Math.
                Theor. 42 (31), 315203.
             Lazovi´ c, G., Vosika, Z., Lazarevi´ c, M., Simi´ c-Krsti´ c, J., Koruga, Ð., 2014. Modeling of bioim-
                pedance for human skin based on fractional distributed-order modified Cole model. FME
                Trans. 42 (1), 74 81.
             Li, Y., Chen, Y., 2011. Theory and implementation of distributed-order element networks.
                ASME 2011 International Design Engineering Technical Conferences and Computers and
                Information in Engineering Conference. American Society of Mechanical Engineers,
                pp. 361 367.
             Li, X.Y., Wu, B.Y., 2016. A numerical method for solving distributed order diffusion equations.
                Appl. Math. Lett. 53, 92 99.
             Li, Y., Sheng, H., Chen,Y.Q., 2010. On distributed order lead-lag compensator, in: Proceedings
                of the 4th IFAC Workshop, Badajoz, Spain.
             Lv, C., Xu, C., 2016. Error analysis of a high order method for time-fractional diffusion equa-
                tions. SIAM J. Sci. Comput. 38 (5), A2699 A2724.
             Mainardi, F., Pagnini, G., 2007. The role of the Fox Wright functions in fractional sub-
                diffusion of distributed order. J. Comput. Appl. Math. 207 (2), 245 257.
             Mainardi, F., Mura, A., Pagnini, G., Gorenflo, R., 2008. Time-fractional diffusion of distributed
                order. J. Vibration Control 14 (9-10), 1267 1290.
             Meerschaert, M.M., Toaldo, B., 2015. Relaxation patterns and semi-markov dynamics. arXiv
                preprint arXiv 1506, 02951.
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