Theory of fractional differantial equations and analysis of dielectric relaxation by using the method of fractional master equation

ABSTRACTMSc. THESISTHEORY OF FRACTIONAL DIFFERANTIAL EQUATIONS ANDANALYSIS OF DIELECTRIC RELAXATION BY USING THE METHOD OFFRACTIONAL MASTER EQUATIONMuhammet Serdar ÇAVUŞDEPARTMENT OF PHYSICSINSTITUE OF NATURAL AND APPLIED SCIENCIESUNIVERSTY OF ÇUKUROVASupervisor: Prof. Dr. Süleyman BOZDEM RYıl: 2006, Pages: 77Jury: Prof. Dr. Süleyman BOZDEM RProf. Dr. Emrullah MEHMETOVAssoc. Prof. Dr. Doğan DÖNMEZIn this study at first fractional order differential calculus technique has beenconsidered; then descriptions and origins of this technique have been examined in detail, theproperties and the methods of the solution are given.By using this technique, a solution of the fractional master equation obtained from theIsing model has been produced, and this solution is applied to the dielectric relaxationprocess. From the solution of the fractional master equation we have obtained the Cole-Coledispersion relation, KWW and algebraic decay relaxation functions. Then these solutions havebeen compared with the ones obtained from the analysis of the Ising model. As a result, it isshown that the solutions obtained from the present fractional master equation are moregeneral than the solutions from the Ising model.Key Words: Fractional Calculus, Dielectric Relaxation, Ising model