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Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial

Citations

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  1. Chunhua Wang & Yufei Li & Gang Yang & Quanli Deng, 2025. "A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks," Mathematics, MDPI, vol. 13(10), pages 1-22, May.
  2. AbdelAty, Amr M. & Fouda, Mohammed E., 2025. "Fractional-order Izhikevich neuron Model: PI-rules numerical simulations and parameter identification," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
  3. Kai Diethelm, 2022. "A New Diffusive Representation for Fractional Derivatives, Part II: Convergence Analysis of the Numerical Scheme," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
  4. Jong Hyuk Byun & Yunil Roh & In-Soo Yoon & Kwang Su Kim & Il Hyo Jung, 2022. "Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model," PLOS ONE, Public Library of Science, vol. 17(11), pages 1-17, November.
  5. Junsheng Duan & Lixia Jing, 2025. "The solution of the time-space fractional diffusion equation based on the Chebyshev collocation method," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(2), pages 489-498, June.
  6. Özköse, Fatma & Yavuz, Mehmet & Şenel, M. Tamer & Habbireeh, Rafla, 2022. "Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
  7. Roman Ivanovich Parovik, 2022. "Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
  8. Margus Lillemäe & Arvet Pedas & Mikk Vikerpuur, 2025. "Central Part Interpolation Approach for Solving Initial Value Problems of Systems of Linear Fractional Differential Equations," Mathematics, MDPI, vol. 13(16), pages 1-19, August.
  9. Telksnienė, Inga & Coccolo, Mattia & Prado-Reynoso, Miguel A. & Čiegis, Raimondas & Sanjuán, Miguel A.F., 2026. "Asymmetric effects of fractional orders on synchronization in a periodically forced FitzHugh–Nagumo system," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
  10. Daniele Mortari & Roberto Garrappa & Luigi Nicolò, 2023. "Theory of Functional Connections Extended to Fractional Operators," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
  11. Mangal, Shiv & Misra, O.P. & Dhar, Joydip, 2023. "Fractional-order deterministic epidemic model for the spread and control of HIV/AIDS with special reference to Mexico and India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 82-102.
  12. Cao, Dewei & Chen, Hu, 2023. "Error analysis of a finite difference method for the distributed order sub-diffusion equation using discrete comparison principle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 109-117.
  13. Paul P. Hager & Dorte Kreher, 2026. "Expanding the rough Heston model in $H$," Papers 2606.16619, arXiv.org.
  14. J. Alberto Conejero & Jonathan Franceschi & Enric Picó-Marco, 2022. "Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide?," Mathematics, MDPI, vol. 10(15), pages 1-18, August.
  15. Fiaz, Muhammad & Aqeel, Muhammad & Marwan, Muhammad & Sabir, Muhammad, 2022. "Integer and fractional order analysis of a 3D system and generalization of synchronization for a class of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
  16. Brugnano, Luigi & Gurioli, Gianmarco & Iavernaro, Felice, 2025. "A shooting-Newton procedure for solving fractional terminal value problems," Applied Mathematics and Computation, Elsevier, vol. 489(C).
  17. Ricardo Almeida, 2025. "A Unified Approach to Implicit Fractional Differential Equations with Anti-Periodic Boundary Conditions," Mathematics, MDPI, vol. 13(17), pages 1-20, September.
  18. Faïçal Ndaïrou & Delfim F. M. Torres, 2023. "Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems," Mathematics, MDPI, vol. 11(19), pages 1-12, October.
  19. Mohammad, Mutaz & Trounev, Alexander, 2025. "Fractal-induced flow dynamics: Viscous flow around Mandelbrot and Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
  20. Sun, Wenkai & Kong, Xianren, 2026. "Statistical analysis of linear oscillators with fractional derivative damping subjected to stationary and nonstationary stochastic excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 681(C).
  21. Vsevolod Bohaienko & Fasma Diele & Carmela Marangi & Cristiano Tamborrino & Sebastian Aleksandrowicz & Edyta Woźniak, 2023. "A Novel Fractional-Order RothC Model," Mathematics, MDPI, vol. 11(7), pages 1-16, March.
  22. Mukhtar, Roshana & Chang, Chuan-Yu & Mukhtar, Aqib & Raja, Muhammad Junaid Ali Asif & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Raja, Muhammad Asif Zahoor, 2025. "A novel fractional Parkinson's disease onset model involving α-syn neuronal transportation and aggregation: A treatise on machine predictive networks," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
  23. Dmytro Sytnyk & Barbara Wohlmuth, 2023. "Exponentially Convergent Numerical Method for Abstract Cauchy Problem with Fractional Derivative of Caputo Type," Mathematics, MDPI, vol. 11(10), pages 1-35, May.
  24. El-Mesady, A. & Elsonbaty, Amr & Adel, Waleed, 2022. "On nonlinear dynamics of a fractional order monkeypox virus model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
  25. Li, Hang & Shen, Yongjun & Han, Yanjun & Dong, Jinlu & Li, Jian, 2023. "Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
  26. Hansin Bilgili & Chwen Sheu, 2022. "A Bibliometric Review of the Mathematics Journal," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
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