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A new fractional operator of variable order: Application in the description of anomalous diffusion

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  1. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
  2. Asifa, & Kumam, Poom & Tassaddiq, Asifa & Watthayu, Wiboonsak & Shah, Zahir & Anwar, Talha, 2022. "Modeling and simulation based investigation of unsteady MHD radiative flow of rate type fluid; a comparative fractional analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 486-507.
  3. Ding, Dawei & Yan, Jie & Wang, Nian & Liang, Dong, 2017. "Pinning synchronization of fractional order complex-variable dynamical networks with time-varying coupling," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 41-50.
  4. Xu, Wei & Liang, Yingjie & Chen, Wen & Wang, Fajie, 2020. "Recent advances of stretched Gaussian distribution underlying Hausdorff fractal distance and its applications in fitting stretched Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
  5. Jinman He & Fangqi Chen & Qinsheng Bi, 2019. "Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network," Complexity, Hindawi, vol. 2019, pages 1-15, April.
  6. Fakhrodin Mohammadi & Hossein Hassani, 2019. "Numerical Solution of Two-Dimensional Variable-Order Fractional Optimal Control Problem by Generalized Polynomial Basis," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 536-555, February.
  7. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
  8. Paul Hauseux & Jack S Hale & Stéphane P A Bordas, 2017. "Calculating the Malliavin derivative of some stochastic mechanics problems," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-18, December.
  9. Zhenduo Sun & Nengneng Qing & Xiangzhi Kong, 2023. "Asymptotic Hybrid Projection Lag Synchronization of Nonidentical Variable-Order Fractional Complex Dynamic Networks," Mathematics, MDPI, vol. 11(13), pages 1-17, June.
  10. Bohaienko, Vsevolod & Gladky, Anatolij & Romashchenko, Mykhailo & Matiash, Tetiana, 2021. "Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm," Applied Mathematics and Computation, Elsevier, vol. 390(C).
  11. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
  12. Riaz, M.B. & Iftikhar, N., 2020. "A comparative study of heat transfer analysis of MHD Maxwell fluid in view of local and nonlocal differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
  13. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
  14. Owolabi, Kolade M. & Atangana, Abdon, 2018. "Chaotic behaviour in system of noninteger-order ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 362-370.
  15. Heydari, M.H. & Razzaghi, M. & Avazzadeh, Z., 2021. "Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrödinger-Boussinesq system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
  16. Razminia, Kambiz & Razminia, Abolhassan & Baleanu, Dumitru, 2019. "Fractal-fractional modelling of partially penetrating wells," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 135-142.
  17. Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.
  18. Rahimkhani, Parisa & Heydari, Mohammad Hossein, 2023. "Fractional shifted Morgan–Voyce neural networks for solving fractal-fractional pantograph differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
  19. Sokhal, Simran & Ram Verma, Sag, 2021. "A Fourier wavelet series solution of partial differential equation through the separation of variables method," Applied Mathematics and Computation, Elsevier, vol. 388(C).
  20. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
  21. Campos, Rafael G. & Huet, Adolfo, 2018. "Numerical inversion of the Laplace transform and its application to fractional diffusion," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 70-78.
  22. Al-khedhairi, A. & Matouk, A.E. & Khan, I., 2019. "Chaotic dynamics and chaos control for the fractional-order geomagnetic field model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 390-401.
  23. Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
  24. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
  25. Hamid Boulares & Abdelkader Moumen & Khaireddine Fernane & Jehad Alzabut & Hicham Saber & Tariq Alraqad & Mhamed Benaissa, 2023. "On Solutions of Fractional Integrodifferential Systems Involving Ψ-Caputo Derivative and Ψ-Riemann–Liouville Fractional Integral," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
  26. Liu, Kui & Wang, JinRong & Zhou, Yong & O’Regan, Donal, 2020. "Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
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