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  1. Fractal green function theory

    Article • Communications in Nonlinear Science and Numerical Simulation, January 2026, Elsevier

    Prof Alireza Khalili Golmankhaneh

  2. On the generalized fractal calculus of variations

    Article • Research in the Mathematical Sciences, December 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  3. About the Fractal Navier–Stokes Equations

    Article • Iranian Journal of Science, December 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  4. Picard’s Method for Solving Fractal Differential Equations

    Article • Acta Applicandae Mathematicae, December 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  5. Fractal functions, self-similar measure and fractal dimensions on the Sierpiński gasket

    Article • Arabian Journal of Mathematics, October 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  6. Fractal Signal Processing

    Article • Circuits Systems and Signal Processing, September 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  7. Fractal Calculus of Variations: A New Framework

    Article • Analysis and Mathematical Physics, September 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  8. Fractal Frenet equations for Fractal curves: a fractal calculus approach

    Article • Boletín de la Sociedad Matemática Mexicana, September 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  9. Homotopy perturbation method for a system of fractal Schrödinger–Korteweg–de Vries equations

    Article • The European Physical Journal Special Topics, July 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  10. Formulation and Quantization of Field Equations on Fractal Space-Time

    Article • International Journal of Theoretical Physics, June 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  11. Fractal calculus: nonhomogeneous linear systems

    Article • Journal of Nonlinear Complex and Data Science, June 2025, De Gruyter

    Prof Alireza Khalili Golmankhaneh

  12. Extending Dirac and Faddeev-Jackiw Formalisms to Fractal First $$\alpha $$-Order Lagrangian Systems

    Article • Complex Analysis and Operator Theory, May 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  13. Fractal Sturm–Liouville problems

    Article • Integral Transforms and Special Functions, May 2025, Taylor & Francis

    Prof Alireza Khalili Golmankhaneh

  14. Solving fractal differential equation via numerical methods

    Article • Arabian Journal of Mathematics, May 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  15. Fractal Sturm–Liouville Theory

    Article • Fractal and Fractional, April 2025, MDPI AG

    Hüseyin Tuna, Prof Alireza Khalili Golmankhaneh

  16. ON HOMOGENEOUS SYSTEM OF FRACTAL DIFFERENTIAL EQUATIONS

    Article • Journal of Mathematical Sciences, March 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  17. Fractal calculus of variations for problems with constraints

    Article • Modern Physics Letters A, February 2025, World Scientific Pub Co Pte Lt

    Professor Palle Jorgensen, Prof Alireza Khalili Golmankhaneh

  18. Fractal Hankel Transform

    Article • Fractal and Fractional, February 2025, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  19. Regular fractal Dirac systems

    Article • International Journal of Geometric Methods in Modern Physics, January 2025, World Scientific Pub Co Pte Lt

    Hüseyin Tuna, Prof Alireza Khalili Golmankhaneh

  20. Fractal Nonlinear Klein-Gordon Equation

    Article • January 2025, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  21. Fractal telegraph equation

    Article • Bollettino dell Unione Matematica Italiana, December 2024, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  22. Fractal Differential Equations of 2α-Order

    Article • Axioms, November 2024, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  23. Analyzing the stability of fractal delay differential equations

    Article • Chaos Solitons & Fractals, November 2024, Elsevier

    Prof Alireza Khalili Golmankhaneh

  24. Higher order fractal differential equations

    Article • Modern Physics Letters A, September 2024, World Scientific Pub Co Pte Lt

    Prof Alireza Khalili Golmankhaneh

  25. Power series solution for fractal differential equations

    Article • Bollettino dell Unione Matematica Italiana, August 2024, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  26. Exact solutions of some fractal differential equations

    Article • Applied Mathematics and Computation, July 2024, Elsevier

    Prof Alireza Khalili Golmankhaneh

  27. Expansion of the universe on fractal time: A study on the dynamics of cosmic growth

    Article • International Journal of Modern Physics A, May 2024, World Scientific Pub Co Pte Lt

    Prof Alireza Khalili Golmankhaneh

  28. Stochastic processes and mean square calculus on fractal curves

    Article • Random Operators and Stochastic Equations, April 2024, De Gruyter

    Prof Alireza Khalili Golmankhaneh

  29. Fractal Schrödinger equation: implications for fractal sets

    Article • Journal of Physics A Mathematical and Theoretical, April 2024, Institute of Physics Publishing

    Prof Alireza Khalili Golmankhaneh

  30. About Sobolev spaces on fractals: fractal gradians and Laplacians

    Article • Aequationes Mathematicae, April 2024, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  31. Einstein field equations extended to fractal manifolds: A fractal perspective

    Article • Journal of Geometry and Physics, February 2024, Elsevier

    Prof Alireza Khalili Golmankhaneh

  32. An s-first return examination on s-sets

    Article • The Journal of Analysis, January 2024, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  33. Dynamics in fractal spaces

    Article • Physics Letters B, January 2024, Elsevier

    Prof Alireza Khalili Golmankhaneh

  34. Modeling tumor growth using fractal calculus: Insights into tumor dynamics

    Article • Biosystems, January 2024, Elsevier

    Prof Alireza Khalili Golmankhaneh

  35. Fractal integral equations

    Article • Journal of Nonlinear Functional Analysis, January 2024, Mathematical Research Press

    Prof Alireza Khalili Golmankhaneh

  36. Fractal Mellin transform and non-local derivatives

    Article • Georgian Mathematical Journal, November 2023, De Gruyter

    Prof Alireza Khalili Golmankhaneh

  37. Fractal Laplace transform: analyzing fractal curves

    Article • The Journal of Analysis, October 2023, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  38. Fractal calculus approach to diffusion on fractal combs

    Article • Chaos Solitons & Fractals, October 2023, Elsevier

    Prof Alireza Khalili Golmankhaneh

  39. On initial value problems of fractal delay equations

    Article • Applied Mathematics and Computation, July 2023, Elsevier

    Prof Alireza Khalili Golmankhaneh

  40. From the Boltzmann equation with non-local correlations to a standard non-linear Fokker-Planck equation

    Article • Physics Letters B, April 2023, Elsevier

    Prof Alireza Khalili Golmankhaneh

  41. Propagation of waves in fractal spaces

    Article • Waves in Random and Complex Media, March 2023, Taylor & Francis

    Prof Alireza Khalili Golmankhaneh

  42. Classical mechanics on fractal curves

    Article • The European Physical Journal Special Topics, February 2023, Springer Science + Business Media

    Prof. Yusif Gasimov, Prof Alireza Khalili Golmankhaneh

  43. Non-standard analysis for fractal calculus

    Article • The Journal of Analysis, January 2023, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  44. On a new generalized local fractal derivative operator

    Article • Chaos Solitons & Fractals, August 2022, Elsevier

    Professor Praveen Agarwal, Prof Alireza Khalili Golmankhaneh

  45. Fractal Calculus and its Applications

    Article • May 2022, World Scientific Pub Co Pte Lt

    Prof Alireza Khalili Golmankhaneh

  46. Nonstandard and fractal electrodynamics in Finsler–Randers space

    Article • International Journal of Geometric Methods in Modern Physics, March 2022, World Scientific Pub Co Pte Lt

    Prof Alireza Khalili Golmankhaneh

  47. Modelling of Electron and Thermal Transport in Quasi-Fractal Carbon Nitride Nanoribbons

    Article • Fractal and Fractional, February 2022, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  48. On Solving Fractional Higher-Order Equations via Artificial Neural Networks

    Article • Iranian Journal of Science and Technology Transactions A Science, February 2022, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  49. Solving fractal differential equations via fractal Laplace transforms

    Article • Journal of Applied Analysis, January 2022, De Gruyter

    Prof Alireza Khalili Golmankhaneh

  50. Hyers–Ulam stability on local fractal calculus and radioactive decay

    Article • The European Physical Journal Special Topics, November 2021, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  51. Laplace equations on the fractal cubes and Casimir effect

    Article • The European Physical Journal Special Topics, November 2021, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  52. Fractal Calculus on Fractal Interpolation Functions

    Article • Fractal and Fractional, October 2021, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  53. General characteristics of a fractal Sturm–Liouville problem

    Article • TURKISH JOURNAL OF MATHEMATICS, July 2021, The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM) - DIGITAL COMMONS JOURNALS

    Prof Alireza Khalili Golmankhaneh

  54. Battery discharging model on fractal time sets

    Article • International Journal of Nonlinear Sciences and Numerical Simulation, June 2021, De Gruyter

    Prof Alireza Khalili Golmankhaneh

  55. Dynamics of particles in cold electrons plasma: fractional actionlike variational approach versus fractal spaces approach

    Article • Waves in Random and Complex Media, April 2021, Taylor & Francis

    Prof Alireza Khalili Golmankhaneh

  56. Generalized heat diffusion equations with variable coefficients and their fractalization from the Black-Scholes equation

    Article • Communications in Theoretical Physics, March 2021, Institute of Physics Publishing

    Prof Alireza Khalili Golmankhaneh

  57. Fractal Stochastic Processes on Thin Cantor-Like Sets

    Article • Mathematics, March 2021, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  58. Electrical circuits involving fractal time

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, March 2021, American Institute of Physics

    Prof Alireza Khalili Golmankhaneh

  59. The Nonlocal Fractal Integral Reverse Minkowski’s and Other Related Inequalities on Fractal Sets

    Article • Mathematical Problems in Engineering, February 2021, Hindawi Publishing Corporation

    Prof Alireza Khalili Golmankhaneh

  60. On fractional and fractal Einstein’s field equations

    Article • Modern Physics Letters A, January 2021, World Scientific Pub Co Pte Lt

    Prof Alireza Khalili Golmankhaneh

  61. Tsallis entropy on fractal sets

    Article • Journal of Taibah University for Science, January 2021, Taylor & Francis

    Prof Alireza Khalili Golmankhaneh

  62. On stability of a class of second alpha-order fractal differential equations

    Article • AIMS Mathematics, January 2020, American Institute of Mathematical Sciences (AIMS)

    Prof Alireza Khalili Golmankhaneh

  63. Stochastic differential equations on fractal sets

    Article • Stochastics, December 2019, Taylor & Francis

    Prof Alireza Khalili Golmankhaneh

  64. Fractal Logistic Equation

    Article • Fractal and Fractional, July 2019, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  65. Random Variables and Stable Distributions on Fractal Cantor Sets

    Article • Fractal and Fractional, June 2019, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  66. Sumudu transform in fractal calculus

    Article • Applied Mathematics and Computation, June 2019, Elsevier

    Prof Alireza Khalili Golmankhaneh

  67. Analogues to Lie Method and Noether’s Theorem in Fractal Calculus

    Article • Fractal and Fractional, May 2019, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  68. Statistical Mechanics Involving Fractal Temperature

    Article • Fractal and Fractional, April 2019, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  69. On the Fractal Langevin Equation

    Article • Fractal and Fractional, March 2019, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  70. Fractal Calculus of Functions on Cantor Tartan Spaces

    Article • Fractal and Fractional, December 2018, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  71. On artificial neural networks approach with new cost functions

    Article • Applied Mathematics and Computation, December 2018, Elsevier

    Prof Alireza Khalili Golmankhaneh

  72. About Kepler’s Third Law on fractal-time spaces

    Article • Ain Shams Engineering Journal, December 2018, Elsevier

    Prof Alireza Khalili Golmankhaneh

  73. Diffusion on Middle-ξ Cantor Sets

    Article • Entropy, July 2018, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  74. Noteworthy fractal features and transport properties of Cantor tartans

    Article • Physics Letters A, June 2018, Elsevier

    Prof Alireza Khalili Golmankhaneh

  75. Sub- and super-diffusion on Cantor sets: Beyond the paradox

    Article • Physics Letters A, April 2018, Elsevier

    Prof Alireza Khalili Golmankhaneh

  76. PSO and NN modeling for photocatalytic removal of pollution in wastewater

    Article • October 2017, Institute of Electrical & Electronics Engineers (IEEE)

    Prof Alireza Khalili Golmankhaneh

  77. Energy Straggling Function by Fα-Calculus

    Article • Journal of Computational and Nonlinear Dynamics, May 2017, ASME International

    Prof Alireza Khalili Golmankhaneh

  78. On the Lipschitz condition in the fractal calculus

    Article • Chaos Solitons & Fractals, February 2017, Elsevier

    Prof Alireza Khalili Golmankhaneh

  79. Using ANNs Approach for Solving Fractional Order Volterra Integro-differential Equations

    Article • International Journal of Computational Intelligence Systems, January 2017, Atlantis Press

    Prof Alireza Khalili Golmankhaneh

  80. On the calculus of parameterized fractal curves

    Article • TURKISH JOURNAL OF PHYSICS, January 2017, The Scientific and Technological Research Council of Turkey

    Prof Alireza Khalili Golmankhaneh

  81. Fractal calculus involving gauge function

    Article • Communications in Nonlinear Science and Numerical Simulation, August 2016, Elsevier

    Prof Alireza Khalili Golmankhaneh

  82. Diffraction from fractal grating Cantor sets

    Article • Journal of Modern Optics, February 2016, Taylor & Francis

    Prof Alireza Khalili Golmankhaneh

  83. New Derivatives on the Fractal Subset of Real-Line

    Article • Entropy, January 2016, MDPI AG

    Prof Alireza Khalili Golmankhaneh

  84. Non-local Integrals and Derivatives on Fractal Sets with Applications

    Article • Open Physics, January 2016, De Gruyter

    Professor Dumitru Baleanu, Prof Alireza Khalili Golmankhaneh

  85. Brand Dynamics: A Case Study

    Article • SSRN Electronic Journal, January 2016, Elsevier

    Prof Alireza Khalili Golmankhaneh

  86. Calculus on Fractals

    Article • January 2015, De Gruyter

    Prof Alireza Khalili Golmankhaneh

  87. quantum mechanics on fractal time-space

    Article • International Journal of Theoretical Physics, September 2014, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  88. About fuzzy Schrödinger equation

    Article • June 2014, Institute of Electrical & Electronics Engineers (IEEE)

    Prof Alireza Khalili Golmankhaneh

  89. Solving fully fuzzy polynomials using feed-back neural networks

    Article • International Journal of Computer Mathematics, May 2014, Taylor & Francis

    Prof Alireza Khalili Golmankhaneh

  90. On Bernstein Polynomials Method to the System of Abel Integral Equations

    Article • Abstract and Applied Analysis, January 2014, Hindawi Publishing Corporation

    Prof Alireza Khalili Golmankhaneh

  91. On Fuzzy Fractional Laplace Transformation

    Article • Advances in Mathematical Physics, January 2014, Hindawi Publishing Corporation

    Prof Alireza Khalili Golmankhaneh

  92. Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets

    Article • Abstract and Applied Analysis, January 2014, Hindawi Publishing Corporation

    Prof Alireza Khalili Golmankhaneh, Prof. Dr. Hari Mohan Srivastava

  93. Synchronization in a nonidentical fractional order of a proposed modified system

    Article • Journal of Vibration and Control, July 2013, SAGE Publications

    Prof Alireza Khalili Golmankhaneh

  94. Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line

    Article • International Journal of Theoretical Physics, July 2013, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  95. Analytic Solution for a Nonlinear Problem of Magneto-Thermoelasticity

    Article • Reports on Mathematical Physics, June 2013, Elsevier

    Prof Alireza Khalili Golmankhaneh

  96. About Maxwell’s equations on fractal subsets of ℝ3

    Article • Open Physics, January 2013, De Gruyter

    Prof Alireza Khalili Golmankhaneh

  97. On a new measure on fractals

    Article • Journal of Inequalities and Applications, January 2013, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  98. The Proposed Modified Liu System with Fractional Order

    Article • Advances in Mathematical Physics, January 2013, Hindawi Publishing Corporation

    Prof Alireza Khalili Golmankhaneh

  99. Numerical solution of linear integral equations system using the Bernstein collocation method

    Article • Advances in Difference Equations, January 2013, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  100. On the Fractional Hamilton and Lagrange Mechanics

    Article • International Journal of Theoretical Physics, April 2012, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  101. Structure of magnetic field lines

    Article • Communications in Nonlinear Science and Numerical Simulation, February 2012, Elsevier

    Prof Alireza Khalili Golmankhaneh

  102. Comparison of iterative methods by solving nonlinear Sturm-Liouville, Burgers and Navier-Stokes equations

    Article • Open Physics, January 2012, De Gruyter

    Prof Alireza Khalili Golmankhaneh

  103. On nonlinear fractional Klein–Gordon equation

    Article • Signal Processing, March 2011, Elsevier

    Prof Alireza Khalili Golmankhaneh

  104. The Fractional Virial Theorem

    Article • Fractional Differential Calculus, January 2011, Element d.o.o.

    Prof Alireza Khalili Golmankhaneh

  105. Fractional Odd-Dimensional Mechanics

    Article • Advances in Difference Equations, January 2011, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  106. On electromagnetic field in fractional space

    Article • Nonlinear Analysis Real World Applications, February 2010, Elsevier

    Prof Alireza Khalili Golmankhaneh

  107. Fractional Newtonian mechanics

    Article • Open Physics, January 2010, De Gruyter

    Professor Dumitru Baleanu, Prof Alireza Khalili Golmankhaneh

  108. On Fractional Dynamics on the Extended Phase Space

    Article • Journal of Computational and Nonlinear Dynamics, January 2010, ASME International

    Prof Alireza Khalili Golmankhaneh

  109. Hamiltonian Structure of Fractional First Order Lagrangian

    Article • International Journal of Theoretical Physics, December 2009, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  110. Relativistic scalar fields for non-conservative systems

    Article • Physica Scripta, October 2009, Institute of Physics Publishing

    Prof Alireza Khalili Golmankhaneh

  111. Newtonian law with memory

    Article • Nonlinear Dynamics, August 2009, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  112. Fractional Electromagnetic Equations Using Fractional Forms

    Article • International Journal of Theoretical Physics, August 2009, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  113. The Dual Action of Fractional Multi Time Hamilton Equations

    Article • International Journal of Theoretical Physics, May 2009, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh

  114. Fractional Mechanics on the Extended Phase Space

    Article • January 2009, ASME International

    Prof Alireza Khalili Golmankhaneh

  115. Fractional Nambu Mechanics

    Article • International Journal of Theoretical Physics, October 2008, Springer Science + Business Media

    Prof Alireza Khalili Golmankhaneh