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Mittag-Leffler Functions and Their Applications

Citations

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Cited by:

  1. Sara H. M. Hamed & Eltayeb A. Yousif & Arbab I. Arbab, 2014. "Analytic and Approximate Solutions of the Space‐Time Fractional Schrödinger Equations by Homotopy Perturbation Sumudu Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
  2. Luisa Beghin & Claudio Macci, 2012. "Alternative Forms of Compound Fractional Poisson Processes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
  3. 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.
  4. 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.
  5. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
  6. 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.
  7. 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.
  8. Giacomo Ascione & Nikolai Leonenko & Enrica Pirozzi, 2018. "Fractional Queues with Catastrophes and Their Transient Behaviour," Mathematics, MDPI, vol. 6(9), pages 1-26, September.
  9. Yun Chen-Shue & Yukun Li & Jiongmin Yong, 2024. "A Limit Order Book Model for High Frequency Trading with Rough Volatility," Papers 2412.16850, arXiv.org.
  10. 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.
  11. 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.
  12. Goswami, Koushik, 2021. "Work fluctuations in a generalized Gaussian active bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
  13. Jung, Jae Won & Seo, Sung Kyu & Kim, Kyungsik, 2025. "Joint probability densities of an active particle coupled to two heat reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 668(C).
  14. Bakalis, Evangelos & Zerbetto, Francesco, 2025. "Barrier-crossing driven by fractional Gaussian noise in the context of reactive flux formalism: An exact result," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 661(C).
  15. Rohini Bhagwanrao Pote & Kuldeep Kumar Kataria, 2025. "On Erlang Queue with Multiple Arrivals and its Time-Changed Variant," Methodology and Computing in Applied Probability, Springer, vol. 27(3), pages 1-36, September.
  16. 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.
  17. dos Santos, Maike A.F., 2020. "Mittag-Leffler functions in superstatistics," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
  18. 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.
  19. Anthony G. Pakes, 2025. "On the Stationary Measure for Markov Branching Processes," Mathematics, MDPI, vol. 13(11), pages 1-27, May.
  20. 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).
  21. Gauhar Rahman & Abdus Saboor & Zunaira Anjum & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "An Extension of the Mittag‐Leffler Function and Its Associated Properties," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
  22. 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.
  23. Marko Kostić, 2013. "Perturbation Theory for Abstract Volterra Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
  24. 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.
  25. 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).
  26. 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.
  27. 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).
  28. Om Ahuja & Asena Çetinkaya & Naveen Kumar Jain, 2022. "Mittag‐Leffler Operator Connected with Certain Subclasses of Bazilevic̆ Functions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
  29. Zhokh, O.O. & Strizhak, P.E., 2026. "A review of non-fickian reaction-diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
  30. 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.
  31. Ascione, Giacomo & Leonenko, Nikolai & Pirozzi, Enrica, 2020. "Fractional Erlang queues," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3249-3276.
  32. 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.
  33. Iomin, A., 2016. "Quantum continuous time random walk in nonlinear Schrödinger equation with disorder," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 64-70.
  34. Yana A. Butko & Merten Mlinarzik, 2026. "Fractional Itô Calculus for Randomly Scaled Fractional Brownian Motion and its Applications to Evolution Equations," Journal of Theoretical Probability, Springer, vol. 39(2), pages 1-45, June.
  35. 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).
  36. Tomas Skovranek, 2019. "The Mittag-Leffler Fitting of the Phillips Curve," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
  37. 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).
  38. 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 Mar 2026.
  39. B. B. Jaimini & Meenu & Suman Sharma & S. D. Purohit & D. L. Suthar, 2025. "A General Class of Multivariable Mittag–Leffler Function and Its Associated Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2025(1).
  40. 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.
  41. Johannes Muhle-Karbe & Youssef Ouazzani Chahdi & Mathieu Rosenbaum & Gr'egoire Szymanski, 2026. "A unified theory of order flow, market impact, and volatility," Papers 2601.23172, arXiv.org, revised Feb 2026.
  42. 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.
  43. 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.
  44. 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.
  45. Edgardo Alvarez-Pardo & Carlos Lizama, 2012. "The Maximal Subspace for Generation of (a, k)‐Regularized Families," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
  46. Giacomo Ascione & Enrica Pirozzi, 2020. "On the Construction of Some Fractional Stochastic Gompertz Models," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
  47. José Francisco Gómez Aguilar & Margarita Miranda Hernández, 2014. "Space‐Time Fractional Diffusion‐Advection Equation with Caputo Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
  48. Youssef Ouazzani Chahdi & Mathieu Rosenbaum & Gr'egoire Szymanski, 2024. "A theory of passive market impact," Papers 2412.07461, arXiv.org.
  49. Sergei Rogosin, 2015. "The Role of the Mittag-Leffler Function in Fractional Modeling," Mathematics, MDPI, vol. 3(2), pages 1-14, May.
  50. Ibtisam Aldawish & Mallikarjun G. Shrigan & Sheza El-Deeb & Hari M. Srivastava, 2025. "On Bi-Univalent Function Classes Defined via Gregory Polynomials," Mathematics, MDPI, vol. 13(19), pages 1-10, September.
  51. 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.
  52. 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.
  53. 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).
  54. Edgardo Alvarez & Carlos Lizama, 2020. "The Super-Diffusive Singular Perturbation Problem," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
  55. 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.
  56. 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.
  57. Virginia Kiryakova, 2021. "A Guide to Special Functions in Fractional Calculus," Mathematics, MDPI, vol. 9(1), pages 1-40, January.
  58. 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.
  59. 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.
  60. 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.
  61. Gajda, Janusz & Beghin, Luisa, 2021. "Prabhakar Lévy processes," Statistics & Probability Letters, Elsevier, vol. 178(C).
  62. Daniele Mortari, 2023. "Representation of Fractional Operators Using the Theory of Functional Connections," Mathematics, MDPI, vol. 11(23), pages 1-16, November.
  63. 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.
  64. Kangqun Zhang, 2020. "Existence of Solution of Space–Time Fractional Diffusion‐Wave Equation in Weighted Sobolev Space," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
  65. 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).
  66. Nozari, Hasan Abbasi & Rostami, Seyed Jalil Sadati & Castaldi, Paolo, 2024. "Unknown-input pseudo-state observer synthesis for fractional-order systems: A geometric framework," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
  67. 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.
  68. 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.
  69. Jim Gatheral & Martin Keller-Ressel, 2019. "Affine forward variance models," Finance and Stochastics, Springer, vol. 23(3), pages 501-533, July.
  70. Neha Gupta & Arun Kumar, 2023. "Fractional Poisson Processes of Order k and Beyond," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2165-2191, December.
  71. 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).
  72. 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.
  73. 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).
  74. 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.
  75. 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.
  76. J. A. Tenreiro Machado, 2013. "Fractional Dynamics of Genetic Algorithms Using Hexagonal Space Tessellation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
  77. Fen Qin & Fuyi Xu & Huizeng Qin, 2022. "Some Notes of the Fractional Integral and Derivatives and Its Applications," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
  78. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
  79. 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.
  80. Nikolai Leonenko & Ely Merzbach, 2015. "Fractional Poisson Fields," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 155-168, March.
  81. 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.
  82. Ahmad A Abubaker & Khaled Matarneh & Suha B. Al-Shaikh & Mohammad Faisal Khan, 2025. "Some new applications of the fractional integral and four-parameter Mittag-Leffler function," PLOS ONE, Public Library of Science, vol. 20(2), pages 1-18, February.
  83. Roman G. Smirnov, 2026. "Caputo-Type Memory Invariants: A Fractional Generalization of the Cobb-Douglas Production Function," Papers 2605.20152, arXiv.org.
  84. 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.
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