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Mittag-Leffler Functions and Their Applications

Citations

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Cited by:

  1. Rakesh K. Parmar, 2015. "A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus," Mathematics, MDPI, vol. 3(4), pages 1-14, November.
  2. Sánchez, Ewin, 2019. "Burr type-XII as a superstatistical stationary distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 443-446.
  3. Virginia Kiryakova & Jordanka Paneva-Konovska, 2024. "Going Next after “A Guide to Special Functions in Fractional Calculus”: A Discussion Survey," Mathematics, MDPI, vol. 12(2), pages 1-39, January.
  4. Serkan Araci & Gauhar Rahman & Abdul Ghaffar & Azeema & Kottakkaran Sooppy Nisar, 2019. "Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
  5. Ravi Agarwal & Snezhana Hristova & Donal O’Regan & Peter Kopanov, 2020. "p -Moment Mittag–Leffler Stability of Riemann–Liouville Fractional Differential Equations with Random Impulses," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
  6. Das, Meghadri & Samanta, G.P., 2020. "A delayed fractional order food chain model with fear effect and prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 218-245.
  7. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
  8. Giacomo Ascione & Enrica Pirozzi, 2020. "On the Construction of Some Fractional Stochastic Gompertz Models," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
  9. Thomas R. Barrick & Catherine A. Spilling & Matt G. Hall & Franklyn A. Howe, 2021. "The Mathematics of Quasi-Diffusion Magnetic Resonance Imaging," Mathematics, MDPI, vol. 9(15), pages 1-23, July.
  10. Najma Ahmed & Nehad Ali Shah & Farman Ali & Dumitru Vieru & F.D. Zaman, 2021. "Analytical Solutions of the Fractional Mathematical Model for the Concentration of Tumor Cells for Constant Killing Rate," Mathematics, MDPI, vol. 9(10), pages 1-14, May.
  11. Youssef Ouazzani Chahdi & Mathieu Rosenbaum & Gr'egoire Szymanski, 2024. "A theory of passive market impact," Papers 2412.07461, arXiv.org.
  12. Sergei Rogosin, 2015. "The Role of the Mittag-Leffler Function in Fractional Modeling," Mathematics, MDPI, vol. 3(2), pages 1-14, May.
  13. Sánchez C., Ewin & Vega-Jorquera, Pedro, 2019. "Modelling temporal decay of aftershocks by a solution of the fractional reactive equation," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 43-49.
  14. Xiong, Xiangtuan & Xue, Xuemin, 2019. "A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 292-303.
  15. Giacomo Ascione & Nikolai Leonenko & Enrica Pirozzi, 2018. "Fractional Queues with Catastrophes and Their Transient Behaviour," Mathematics, MDPI, vol. 6(9), pages 1-26, September.
  16. Kassim, Mohammed D. & Tatar, Nasser-eddine, 2021. "Nonlinear fractional distributed Halanay inequality and application to neural network systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
  17. 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.
  18. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
  19. Goswami, Koushik, 2021. "Work fluctuations in a generalized Gaussian active bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
  20. Edgardo Alvarez & Carlos Lizama, 2020. "The Super-Diffusive Singular Perturbation Problem," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
  21. Soma Dhar & Lipi B. Mahanta & Kishore Kumar Das, 2019. "Formulation Of The Simple Markovian Model Using Fractional Calculus Approach And Its Application To Analysis Of Queue Behaviour Of Severe Patients," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 117-129, March.
  22. Mansour F. Yassen & Adel A. Attiya, 2023. "Certain Quantum Operator Related to Generalized Mittag–Leffler Function," Mathematics, MDPI, vol. 11(24), pages 1-15, December.
  23. Dhar Soma & Mahanta Lipi B. & Das Kishore Kumar, 2019. "Formulation Of The Simple Markovian Model Using Fractional Calculus Approach And Its Application To Analysis Of Queue Behaviour Of Severe Patients," Statistics in Transition New Series, Statistics Poland, vol. 20(1), pages 117-129, March.
  24. Virginia Kiryakova, 2021. "A Guide to Special Functions in Fractional Calculus," Mathematics, MDPI, vol. 9(1), pages 1-40, January.
  25. dos Santos, Maike A.F., 2020. "Mittag-Leffler functions in superstatistics," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
  26. Bruno Durin & Mathieu Rosenbaum & Gr'egoire Szymanski, 2023. "The two square root laws of market impact and the role of sophisticated market participants," Papers 2311.18283, arXiv.org.
  27. Jessica Mendiola-Fuentes & Eugenio Guerrero-Ruiz & Juan Rosales-García, 2024. "Multivariate Mittag-Leffler Solution for a Forced Fractional-Order Harmonic Oscillator," Mathematics, MDPI, vol. 12(10), pages 1-11, May.
  28. Saif Eddin Jabari & Nikolaos M. Freris & Deepthi Mary Dilip, 2020. "Sparse Travel Time Estimation from Streaming Data," Transportation Science, INFORMS, vol. 54(1), pages 1-20, January.
  29. Michelitsch, Thomas M. & Polito, Federico & Riascos, Alejandro P., 2021. "On discrete time Prabhakar-generalized fractional Poisson processes and related stochastic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
  30. Praveendra Singh & Madhu Jain, 2024. "Inventory policy for degrading items under advanced payment with price and memory sensitive demand using metaheuristic techniques," Operational Research, Springer, vol. 24(3), pages 1-34, September.
  31. Charles K. Amponsah & Tomasz J. Kozubowski & Anna K. Panorska, 2021. "A general stochastic model for bivariate episodes driven by a gamma sequence," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-31, December.
  32. Gajda, Janusz & Beghin, Luisa, 2021. "Prabhakar Lévy processes," Statistics & Probability Letters, Elsevier, vol. 178(C).
  33. Daniele Mortari, 2023. "Representation of Fractional Operators Using the Theory of Functional Connections," Mathematics, MDPI, vol. 11(23), pages 1-16, November.
  34. Katarzyna Górska & Andrzej Horzela, 2021. "Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character," Mathematics, MDPI, vol. 9(5), pages 1-13, February.
  35. Ben Makhlouf, Abdellatif & Benjemaa, Mondher & Boucenna, Djalal & Hammami, Mohamed Ali, 2023. "Darboux problem for proportional partial fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
  36. Slawomir Blasiak, 2021. "Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach," Energies, MDPI, vol. 14(17), pages 1-13, September.
  37. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "A Fractional Ordered COVID-19 Model Incorporating Comorbidity and Vaccination," Mathematics, MDPI, vol. 9(21), pages 1-27, November.
  38. Jim Gatheral & Martin Keller-Ressel, 2019. "Affine forward variance models," Finance and Stochastics, Springer, vol. 23(3), pages 501-533, July.
  39. Angstmann, C.N. & Henry, B.I. & Jacobs, B.A. & McGann, A.V., 2017. "A time-fractional generalised advection equation from a stochastic process," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 175-183.
  40. Hainaut, Donatien, 2021. "Lévy interest rate models with a long memory," LIDAM Discussion Papers ISBA 2021020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  41. Oana Brandibur & Roberto Garrappa & Eva Kaslik, 2021. "Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
  42. Sweilam, N.H. & El-Sakout, D.M. & Muttardi, M.M., 2020. "Numerical study for time fractional stochastic semi linear advection diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
  43. Aghalaya S. Vatsala & Bhuvaneswari Sambandham, 2024. "Remarks on Sequential Caputo Fractional Differential Equations with Fractional Initial and Boundary Conditions," Mathematics, MDPI, vol. 12(24), pages 1-16, December.
  44. Michelitsch, Thomas M. & Riascos, Alejandro P., 2020. "Continuous time random walk and diffusion with generalized fractional Poisson process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
  45. Richard L. Magin & Ervin K. Lenzi, 2021. "Slices of the Anomalous Phase Cube Depict Regions of Sub- and Super-Diffusion in the Fractional Diffusion Equation," Mathematics, MDPI, vol. 9(13), pages 1-29, June.
  46. Tawfik, Ashraf M. & Fichtner, Horst & Elhanbaly, A. & Schlickeiser, Reinhard, 2018. "Analytical solution of the space–time fractional hyperdiffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 178-187.
  47. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
  48. Kumar, Pushpendra & Erturk, Vedat Suat & Vellappandi, M. & Trinh, Hieu & Govindaraj, V., 2022. "A study on the maize streak virus epidemic model by using optimized linearization-based predictor-corrector method in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
  49. Iomin, A. & Zaburdaev, V. & Pfohl, T., 2016. "Reaction front propagation of actin polymerization in a comb-reaction system," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 115-122.
  50. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model," Mathematics, MDPI, vol. 9(7), pages 1-34, March.
  51. Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.
  52. Ascione, Giacomo & Leonenko, Nikolai & Pirozzi, Enrica, 2020. "Fractional Erlang queues," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3249-3276.
  53. Murat A. Sultanov & Durdimurod K. Durdiev & Askar A. Rahmonov, 2021. "Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
  54. Alexander Apelblat, 2020. "Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach," Mathematics, MDPI, vol. 8(5), pages 1-22, April.
  55. Iomin, A., 2016. "Quantum continuous time random walk in nonlinear Schrödinger equation with disorder," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 64-70.
  56. Kar, Silajit & Maiti, Dilip K. & Maiti, Atasi Patra, 2024. "Impacts of non-locality and memory kernel of fractional derivative, awareness and treatment strategies on HIV/AIDS prevalence," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
  57. Tomas Skovranek, 2019. "The Mittag-Leffler Fitting of the Phillips Curve," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
  58. Hees, Katharina & Nayak, Smarak & Straka, Peter, 2021. "Statistical inference for inter-arrival times of extreme events in bursty time series," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
  59. Hari M. Srivastava & Arran Fernandez & Dumitru Baleanu, 2019. "Some New Fractional-Calculus Connections between Mittag–Leffler Functions," Mathematics, MDPI, vol. 7(6), pages 1-10, May.
  60. Ulrich Horst & Wei Xu & Rouyi Zhang, 2023. "Convergence of Heavy-Tailed Hawkes Processes and the Microstructure of Rough Volatility," Papers 2312.08784, arXiv.org, revised Nov 2024.
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