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    Analysis of charge variation in fractional order LC electrical circuit
    (Soc Mexicana Fisica, 2016) Calik, A. E.; Sirin, H.; Ertik, H.; Sen, M.
    In this paper, the charge variation in time has been investigated in electrical LC circuit within the framework of fractional calculus. The second order differential equation related to the LC circuit has been re-solved by using Caputo fractional derivative. The solution of this new equation has been obtained in terms of Mittag-Leffier function which behaves in between power law and exponential law forms. The order of time-fractional derivative characterizes the time fractality effects in the system, and is considered in the interval 1 < alpha < 2. The obtained results have been compared with the other studies in the literature. It has been concluded that the Mittag-Leffier function and the order of time-fractional derivative have a special importance to take into account the non-local behaviour of the physical process in time.
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    A fractional mathematical approach to the distribution functions of quantum gases: Cosmic Microwave Background Radiation problem is revisited
    (Elsevier Science Bv, 2009) Ertik, H.; Demirhan, D.; Sirin, H.; Buyukkilic, F.
    Efforts on the fundamentals of the nonextensive thermostatistical formulations of the realistic description of the physical systems have always been underway. In this context, the quantum systems of bosons and fermions are taken into consideration as g-ons. A new formalism of the unified distribution functions has been introduced using a fractional mathematical approach. With the purpose of verification of the theory, blackbody radiation problem has been investigated by making use of the generalized fractional Planck's distribution. In this context, the observed Cosmic Microwave Background Radiation (CMBR) energy density could be obtained exactly within nonextensive thermostatistical approach for the value alpha = 0.999983 of the order of the fractional derivative and for the blackbody temperature T = 2.72818 K. (C) 2009 Elsevier B.V. All rights reserved.
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    A fractional mathematical approach to the distribution functions of quantum gases: Cosmic Microwave Background Radiation problem is revisited
    (Elsevier Science Bv, 2009) Ertik, H.; Demirhan, D.; Sirin, H.; Buyukkilic, F.
    Efforts on the fundamentals of the nonextensive thermostatistical formulations of the realistic description of the physical systems have always been underway. In this context, the quantum systems of bosons and fermions are taken into consideration as g-ons. A new formalism of the unified distribution functions has been introduced using a fractional mathematical approach. With the purpose of verification of the theory, blackbody radiation problem has been investigated by making use of the generalized fractional Planck's distribution. In this context, the observed Cosmic Microwave Background Radiation (CMBR) energy density could be obtained exactly within nonextensive thermostatistical approach for the value alpha = 0.999983 of the order of the fractional derivative and for the blackbody temperature T = 2.72818 K. (C) 2009 Elsevier B.V. All rights reserved.
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    The influence of fractality on the time evolution of the diffusion process
    (Elsevier Science Bv, 2010) Sirin, H.; Buyukkilic, F.; Ertik, H.; Demirhan, D.
    In the literature, the deviations from standard behaviors of the solutions of the kinetic equation and the analogous diffusion equation are put forward by investigations which are carried out in the frame of fractional mathematics and nonextensive physics On the other hand, the physical origins of the order of derivative namely a in fractional mathematics and the entropy index q in nonextensive physics are a topic of interest in scientific media. In this study, the solutions of the diffusion equation which have been obtained in the framework of fractional mathematics and nonextensive physics are revised. The diffusion equation is solved by the cumulative diminuation/growth method which has been developed by two of the present authors and physical nature of the parameters a and q are enlightened in connection with fractality of space and the memory effect It has been emphasized that the mathematical basis of deviations from standard behavior in the distribution functions could be established by fractional mathematics where as the physical mechanism could be revealed using the cumulative diminuation/growth method (C) 2010 Elsevier B.V. All rights reserved
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    Investigation of electrical RC circuit within the framework of fractional calculus
    (Soc Mexicana Fisica, 2015) Ertik, H.; Calik, A. E.; Sirin, H.; Sen, M.; Oder, B.
    In this paper, charging and discharging processes of different capacitors in electrical RC circuit are considered theoretically and experimentally. The non-local behaviors in these processes, arising from the time fractality, are investigated via fractional calculus. In this context, the time fractional differential equation related to electrical RC circuit is proposed by making use of Caputo fractional derivative. The resulting solution exhibits a feature in between power law and exponential law forms, and is obtained in terms of Mittag-Leffler function which describes physical systems with memory. The order of fractional derivative characterizes the fractality of time and being considered in the interval 0 < alpha <= 1. The traditional conclusions are recovered for alpha = 1, where time becomes homogenous and system has Markovian nature. By using time fractional approach, the discrepancies between the experimentally measured data and the theoretical calculations have been removed.
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