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      Nonlocal Cauchy problem for fractional evolution equations

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      Nonlinear Analysis: Real World Applications
      Elsevier BV

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          Fractional diffusion and wave equations

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            Basic theory of fractional differential equations

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              A fractional calculus approach to self-similar protein dynamics.

              Relaxation processes and reaction kinetics of proteins deviate from exponential behavior because of their large amount of conformational substrates. The dynamics are governed by many time scales and, therefore, the decay of the relaxation function or reactant concentration is slower than exponential. Applying the idea of self-similar dynamics, we derive a fractal scaling model that results in an equation in which the time derivative is replaced by a differentiation (d/dt)beta of non-integer order beta. The fractional order differential equation is solved by a Mittag-Leffler function. It depends on two parameters, a fundamental time scale tau 0 and a fractional order beta that can be interpreted as a self-similarity dimension of the dynamics. Application of the fractal model to ligand rebinding and pressure release measurements of myoglobin is demonstrated, and the connection of the model to considerations of energy barrier height distributions is shown.
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                Author and article information

                Journal
                Nonlinear Analysis: Real World Applications
                Nonlinear Analysis: Real World Applications
                Elsevier BV
                14681218
                October 2010
                October 2010
                : 11
                : 5
                : 4465-4475
                Article
                10.1016/j.nonrwa.2010.05.029
                4a378730-d08a-4650-9057-feb3174549e6
                © 2010

                http://www.elsevier.com/tdm/userlicense/1.0/

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