Determination of non-conservative systems by using fractional calculus and application to some problems

There are many advantages to descripe nature by using calculus of variations instead of the approach developed by Newton. However, although much processes in the physical world are non-conservative, it is not possible to directly apply the Euler-Lagrange equation achieved using standard mathematics to the non-conservative systems. which is derived by standart mahetmatic equations. It is possible to generalize the Euler-Lagrange equations to include non-conservative systems by using franctional mathematics. By this method developed, the effect of memory is not neglected unlike the standard mathematics. In this study, Euler-Lagrange equations which are achieved by using fractional mathematics are transformed into standard equations where the fractional derivative is equal to the order of the derivative. Additionally, the results obtained by the fractional Euler-Lagrange equation are generalized to the results obtained by the standard equation, and the standart result is obtained when the fractional derivative is equal to the individual. In this context, the problem of fractional harmonic osscilator is discussed, its solutions are examine and it is shown the standard results of the achieved results are generalized