All Stories

  1. Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models
  2. Logistic equation with continuously distributed lag and application in economics
  3. On History of Mathematical Economics: Application of Fractional Calculus
  4. Self-organization with memory
  5. Dynamic Keynesian Model of Economic Growth with Memory and Lag
  6. Harrod–Domar Growth Model with Memory and Distributed Lag
  7. Macroeconomic models with long dynamic memory: Fractional calculus approach
  8. Generalized Memory: Fractional Calculus Approach
  9. No nonlocality. No fractional derivative
  10. Criterion of Existence of Power-Law Memory for Economic Processes
  11. Fractional Derivative Regularization in QFT
  12. Exact Discretization of an Economic Accelerator and Multiplier with Memory
  13. Interpretation of Fractional Derivatives as Reconstruction from Sequence of Integer Derivatives
  14. Logistic map with memory from economic model
  15. Exact discretization of fractional Laplacian
  16. Long and Short Memory in Economics: Fractional-Order Difference and Differentiation
  17. Exact Solution of T-Difference Radial Schrödinger Equation
  18. Poiseuille equation for steady flow of fractal fluid
  19. Some Identities with Generalized Hypergeometric Functions
  20. FRACTIONAL-ORDER VARIATIONAL DERIVATIVE
  21. Exact discretization by Fourier transforms
  22. Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations
  23. Acoustic waves in fractal media: Non-integer dimensional spaces approach
  24. Electric field in media with power-law spatial dispersion
  25. Heat transfer in fractal materials
  26. United lattice fractional integro-differentiation
  27. Remark to history of fractional derivatives on complex plane: Sonine-Letnikov and Nishimoto derivatives
  28. Exact discretization of Schrödinger equation
  29. Discrete model of dislocations in fractional nonlocal elasticity
  30. On chain rule for fractional derivatives
  31. Fractional Calculus: D’où venons-nous? Que sommes-nous? Où allons-nous?
  32. Geometric interpretation of fractional-order derivative
  33. Elasticity for economic processes with memory: fractional differential calculus approach
  34. Electromagnetic waves in non-integer dimensional spaces and fractals
  35. Leibniz Rule and Fractional Derivatives of Power Functions
  36. Fractional-order difference equations for physical lattices and some applications
  37. Variational principle of stationary action for fractional nonlocal media and fields
  38. Fractal electrodynamics via non-integer dimensional space approach
  39. Comments on “The Minkowski's space–time is consistent with differential geometry of fractional order” [Phys. Lett. A 363 (2007) 5–11]
  40. COMMENTS ON "RIEMANN–CHRISTOFFEL TENSOR IN DIFFERENTIAL GEOMETRY OF FRACTIONAL ORDER APPLICATION TO FRACTAL SPACE-TIME", [FRACTALS 21 (2013) 1350004]
  41. Three-dimensional lattice models with long-range interactions of Grünwald–Letnikov type for fractional generalization of gradient elasticity
  42. Non-standard extensions of gradient elasticity: Fractional non-locality, memory and fractality
  43. Local Fractional Derivatives of Differentiable Functions are Integer-order Derivatives or Zero
  44. Lattice fractional calculus
  45. Lattice Model with Nearest-Neighbor and Next-Nearest-Neighbor Interactions for Gradient Elasticity
  46. Fractional Liouville equation on lattice phase-space
  47. Vector calculus in non-integer dimensional space and its applications to fractal media
  48. Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series
  49. Elasticity of fractal materials using the continuum model with non-integer dimensional space
  50. Flow of fractal fluid in pipes: Non-integer dimensional space approach
  51. Large lattice fractional Fokker–Planck equation
  52. Toward lattice fractional vector calculus
  53. Anisotropic fractal media by vector calculus in non-integer dimensional space
  54. Lattice with long-range interaction of power-law type for fractional non-local elasticity
  55. Non-linear fractional field equations: weak non-linearity at power-law non-locality
  56. General lattice model of gradient elasticity
  57. Lattice model of fractional gradient and integral elasticity: Long-range interaction of Grünwald–Letnikov–Riesz type
  58. Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach
  59. Fractional Gradient Elasticity from Spatial Dispersion Law
  60. Fractional Quantum Field Theory: From Lattice to Continuum
  61. Toward fractional gradient elasticity
  62. No violation of the Leibniz rule. No fractional derivative
  63. Power-law spatial dispersion from fractional Liouville equation
  64. Editorial
  65. Fractional power-law spatial dispersion in electrodynamics
  66. REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELS
  67. Uncertainty relation for non-Hamiltonian quantum systems
  68. Lattice model with power-law spatial dispersion for fractional elasticity
  69. Fractional diffusion equations for open quantum system
  70. Quantum dissipation from power-law memory
  71. The fractional oscillator as an open system
  72. Fractional Dynamics of Open Quantum Systems
  73. Relativistic non-Hamiltonian mechanics
  74. Fractional dissipative standard map
  75. Fractional Dynamics
  76. Fractional Dynamics of Relativistic Particle
  77. Discrete map with memory from fractional differential equation of arbitrary positive order
  78. Fractional standard map
  79. Differential equations with fractional derivative and universal map with memory
  80. Fractional integro-differential equations for electromagnetic waves in dielectric media
  81. Fractional generalization of the quantum Markovian master equation
  82. Conservation laws and Hamilton’s equations for systems with long-range interaction and memory
  83. Fokker–Planck equation with fractional coordinate derivatives
  84. Fractional vector calculus and fractional Maxwell’s equations
  85. Weyl quantization of fractional derivatives
  86. Fractional equations of kicked systems and discrete maps
  87. Universal electromagnetic waves in dielectric
  88. Fractional Heisenberg equation
  89. Fractional equations of Curie–von Schweidler and Gauss laws
  90. Fractional generalization of Kac integral
  91. Chains with the fractal dispersion law
  92. A Very Few Preliminaries
  93. Bibliography
  94. Chapter 1 Quantum Kinematics of Bounded Observables
  95. Chapter 10 Superoperators and its Properties
  96. Chapter 11 Superoperator Algebras and Spaces
  97. Chapter 12 Superoperator Functions
  98. Chapter 13 Semi-Groups of Superoperators
  99. Chapter 14 Differential Equations for Quantum Observables
  100. Chapter 15 Quantum Dynamical Semi-Group
  101. Chapter 16 Classical Non-Hamiltonian Dynamics
  102. Chapter 17 Quantization of Dynamical Structure
  103. Chapter 18 Quantum Dynamics of States
  104. Chapter 19 Dynamical Deformation of Algebras of Observables
  105. Chapter 2 Quantum Kinematics of Unbounded Observables
  106. Chapter 20 Fractional Quantum Dynamics
  107. Chapter 21 Stationary States of Non-Hamiltonian Systems
  108. Chapter 22 Quantum Dynamical Methods
  109. Chapter 23 Path Integral for Non-Hamiltonian Systems
  110. Chapter 24 Non-Hamiltonian Systems as Quantum Computers
  111. Chapter 3 Mathematical Structures in Quantum Kinematics
  112. Chapter 4 Spaces of Quantum Observables
  113. Chapter 5 Algebras of Quantum Observables
  114. Chapter 6 Mathematical Structures on State Sets
  115. Chapter 7 Mathematical Structures in Classical Kinematics
  116. Chapter 8 Quantization in Kinematics
  117. Chapter 9 Spectral Representation of Observable
  118. Preface
  119. Coupled oscillators with power-law interaction and their fractional dynamics analogues
  120. Dynamics of the chain of forced oscillators with long-range interaction: From synchronization to chaos
  121. Fractional dynamics of systems with long-range space interaction and temporal memory
  122. FOKKER–PLANCK EQUATION FOR FRACTIONAL SYSTEMS
  123. FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE
  124. LIOUVILLE AND BOGOLIUBOV EQUATIONS WITH FRACTIONAL DERIVATIVES
  125. THE FRACTIONAL CHAPMAN–KOLMOGOROV EQUATION
  126. Fractional dynamics of systems with long-range interaction
  127. Continuous limit of discrete systems with long-range interaction
  128. Map of discrete system into continuous
  129. Dynamics with low-level fractionality
  130. Nonholonomic constraints with fractional derivatives
  131. ELECTROMAGNETIC FIELDS ON FRACTALS
  132. Fractional variations for dynamical systems: Hamilton and Lagrange approaches
  133. Psi-series solution of fractional Ginzburg–Landau equation
  134. Fractional dynamics of coupled oscillators with long-range interaction
  135. Magnetohydrodynamics of fractal media
  136. TRANSPORT EQUATIONS FROM LIOUVILLE EQUATIONS FOR FRACTIONAL SYSTEMS
  137. Fractional statistical mechanics
  138. Gravitational Field of Fractal Distribution of Particles
  139. DYNAMICS OF FRACTAL SOLIDS
  140. MULTIPOLE MOMENTS OF FRACTAL DISTRIBUTION OF CHARGES
  141. Electromagnetic field of fractal distribution of charged particles
  142. Fractional Ginzburg–Landau equation for fractal media
  143. Fractional hydrodynamic equations for fractal media
  144. Fractional Generalization of Gradient Systems
  145. WAVE EQUATION FOR FRACTAL SOLID STRING
  146. Fractional generalization of gradient and Hamiltonian systems
  147. Fractional Fokker–Planck equation for fractal media
  148. Possible experimental test of continuous medium model for fractal media
  149. Stationary solutions of Liouville equations for non-Hamiltonian systems
  150. Continuous medium model for fractal media
  151. Phase-space metric for non-Hamiltonian systems
  152. THERMODYNAMICS OF FEW-PARTICLE SYSTEMS
  153. Fractional systems and fractional Bogoliubov hierarchy equations
  154. Fractional generalization of Liouville equations
  155. Path integral for quantum operations
  156. CLASSICAL CANONICAL DISTRIBUTION FOR DISSIPATIVE SYSTEMS
  157. Pure stationary states of open quantum systems
  158. Stationary states of dissipative quantum systems
  159. Quantum computer with mixed states and four-valued logic
  160. Quantization of non-Hamiltonian and dissipative systems
  161. Quantum dissipative systems. IV. Analogues of Lie algebras and groups
  162. Quantum dissipative systems. III. Definition and algebraic structure
  163. Quantum dissipative systems. I. Canonical quantization and quantum Liouville equation
  164. TWO-LOOP BETA-FUNCTION FOR NONLINEAR SIGMA-MODEL WITH AFFINE METRIC MANIFOLD
  165. Bosonic string in affine-metric curved space
  166. Ultraviolet finiteness of nonlinear two-dimensional sigma models on affine-metric manifolds