Subordination and memory dependent kinetics in diffusion and relaxation phenomena

Abstract The concept of subordination, originally introduced in the probability and stochastic processes theories, has also appeared analysis evolution equations. So it is not surprising that we meet physics complex systems, particular when study equations describing diffusion dielectric relaxation phenomena. Grace to intuitively understood decomposition into their simpler better known components, called parent leading processes, subordination formalism enables us attribute physical interpretation integral decompositions representing plethora solutions anomalous problems. Moreover, makes investigation properties obeyed by these far easier more effective. Using Laplace-Fourier transform method solve memory-dependent show can be naturally implemented solutions. key achieve this goal use operational calculus merged with application Efros theorem [1]. Adopting exclusively methods classical mathematical are able derive memory-stemmed origin build a bridge connecting functional analysis/operator based solving well established probabilistic approaches. With such developed general hands apply several models