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Communications in nonlinear science & numerical simulation, ISSN 1007-5704, 2013, Volume 18, Issue 11, pp. 2945 - 2948
•A violation of the Leibniz rule is a basic property of fractional derivatives.•Any fractional derivative, which satisfy Leibniz rule, has order equal to... 
Fractional derivative | Leibniz rule | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Computer simulation | Mathematics - Classical Analysis and ODEs
Journal Article
International journal of modern physics. B, Condensed matter physics, statistical physics, applied physics, ISSN 1793-6578, 2013, Volume 27, Issue 9, pp. 1330005 - 1330032
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 08/2014, Volume 55, Issue 8, p. 83510
Journal Article
Annals of Physics, ISSN 0003-4916, 2008, Volume 323, Issue 11, pp. 2756 - 2778
Journal Article
Communications in nonlinear science & numerical simulation, ISSN 1007-5704, 2018, Volume 62, pp. 157 - 163
Journal Article
Journal Article
Wave Motion, ISSN 0165-2125, 06/2016, Volume 63, pp. 18 - 22
Acoustic waves in fractal media are considered in the framework of continuum models with non-integer dimensional spaces. Using recently suggested vector... 
Fractal media | Supersonic mode | Acoustic wave | Non-integer dimensional space | Heterogeneity | Wave motion | Mathematical analysis | Fractal analysis | Media | Fractals | Calculus | Vectors (mathematics)
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 10/2015, Volume 56, Issue 10, p. 103506
Journal Article
Applied mathematics and computation, ISSN 0096-3003, 2015, Volume 257, pp. 12 - 33
Integration and differentiation of non-integer orders for N-dimensional physical lattices with long-range particle interactions are suggested. The proposed... 
Lattice models | Fractional dynamics | Fractional calculus | Fractional integral | Fractional derivative | Nonlocal continuum | LONG-RANGE INTERACTION | MATHEMATICS, APPLIED | DYNAMICS | SYSTEMS | MODEL | Transformations (mathematics) | Integrals | Mathematical analysis | Lattices | Continuums | Differential equations | Mathematical models | Derivatives
Journal Article
Annals of physics, ISSN 0003-4916, 2005, Volume 318, Issue 2, pp. 286 - 307
We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the “fractional” continuous medium model for the... 
Fractal media | Hydrodynamic equations | Fractional integral | POROUS-MEDIA | fractal media | fractional integral | PHYSICS, MULTIDISCIPLINARY | hydrodynamic equations | GEOMETRY | DENSITY | FRACTALS | NAVIER-STOKES EQUATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUILIBRIUM | MASS | SOUND WAVES
Journal Article
Communications in nonlinear science & numerical simulation, ISSN 1007-5704, 2006, Volume 11, Issue 8, pp. 885 - 898
We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/∣ n −... 
Fractional oscillator | Synchronization | Fractional Ginzburg–Landau equation | Long-range interaction | Fractional Ginzburg-Landau equation | Physics - Chaotic Dynamics
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 02/2015, Volume 20, Issue 2, pp. 360 - 374
Journal Article
Chaos, solitons and fractals, ISSN 0960-0779, 2015, Volume 81, pp. 38 - 42
Journal Article
Entropy (Basel, Switzerland), ISSN 1099-4300, 2018, Volume 20, Issue 6, p. 414
Journal Article
International Journal of Solids and Structures, ISSN 0020-7683, 08/2014, Volume 51, Issue 15-16, pp. 2900 - 2907
Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the... 
Fractional dynamics | Fractional elasticity | Long-range interaction | Lattice model | Non-local elasticity | MECHANICS | CALCULUS | MODEL | WAVE-PROPAGATION | Asymptotic properties | Mathematical analysis | Lattices | Continuums | Differential equations | Elasticity | Mathematical models | Derivatives | Physics - Materials Science
Journal Article