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Cited by 16 publications
(9 citation statements)
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“…The joint invariant functions imposed by means of the Stoka theorem allow not only "all possible dynamics" but also "all possible probability densities" associated to these dynamics. Thus, this way is different with respect to that given through fractional derivatives [26,27].…”
Section: Dynamics In a Complex System In The Form Of Schrödinger Typementioning
confidence: 94%
See 1 more Smart Citation
“…The joint invariant functions imposed by means of the Stoka theorem allow not only "all possible dynamics" but also "all possible probability densities" associated to these dynamics. Thus, this way is different with respect to that given through fractional derivatives [26,27].…”
Section: Dynamics In a Complex System In The Form Of Schrödinger Typementioning
confidence: 94%
“…Let us recall that the abovementioned mathematical models are included in motion fractal theories, the dynamics of these theories implying various mathematical procedures (for details see [23][24][25][26][27]). Moreover, the scale relativity theory in Nottale's sense [15] can be accepted as a particular case of the model presented in Appendix A for motion of complex system entities on Peano type curve (i.e., in fractal dimension D F = 2).…”
Section: Short Reminder On the Motion Fractal Theories In The Form Ofmentioning
confidence: 99%
“…This approach associates a time scale with jump distances, and the multiplicity of scales is explicitly taken into account via an integral equation which contains a coupled memory kernel similar to the DO operator [ 212 ]. Other examples of such multifractional processes include the analysis of structures with simultaneous nonlocal and strain-gradient (multiscale) effects [ 213 ], diffusion of particles in microporous materials [ 214 ], analysis of financial markets where distributions of financial data usually possess fast falling power-law tails [ 215 ], and even state functions of complex quantum-mechanical systems [ 216 , 217 ].…”
Section: Relevance Of Distributed-order Operatorsmentioning
confidence: 99%
“…The numerator, given by g(D), also plays a central role here. The D-spherical Schrödinger equation [27] for zero total angular momentum is given by…”
Section: A Less Ideal Case: Three-body System In the Born-oppenheimermentioning
confidence: 99%