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Recent applications of fractional calculus to science and engineering

Citations

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Cited by:

  1. Serik Aitzhanov & Kymbat Bekenayeva & Zamira Abdikalikova, 2023. "Boundary Value Problem for a Loaded Pseudoparabolic Equation with a Fractional Caputo Operator," Mathematics, MDPI, vol. 11(18), pages 1-12, September.
  2. Yousef, Fatma Bozkurt & Yousef, Ali & Maji, Chandan, 2021. "Effects of fear in a fractional-order predator-prey system with predator density-dependent prey mortality," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
  3. Coronel-Escamilla, Antonio & Gomez-Aguilar, Jose Francisco & Stamova, Ivanka & Santamaria, Fidel, 2020. "Fractional order controllers increase the robustness of closed-loop deep brain stimulation systems," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
  4. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
  5. Musrrat Ali & Hemant Gandhi & Amit Tomar & Dimple Singh, 2023. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
  6. Chéagé Chamgoué, A. & Ngueuteu, G.S.M. & Yamapi, R. & Woafo, P., 2018. "Memory effect in a self-sustained birhythmic biological system," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 160-169.
  7. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
  8. Jehad Alzabut & Weerawat Sudsutad & Zeynep Kayar & Hamid Baghani, 2019. "A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
  9. Liu, Haiyu & Lü, Shujuan, 2019. "Galerkin spectral method for nonlinear time fractional Cable equation with smooth and nonsmooth solutions," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 32-47.
  10. Mian Bahadur Zada & Muhammad Sarwar & Thabet Abdeljawad & Aiman Mukheimer, 2021. "Coupled Fixed Point Results in Banach Spaces with Applications," Mathematics, MDPI, vol. 9(18), pages 1-12, September.
  11. Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
  12. Lashkarian, Elham & Reza Hejazi, S., 2017. "Group analysis of the time fractional generalized diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 572-579.
  13. Anague Tabejieu, L.M. & Nana Nbendjo, B.R. & Filatrella, G., 2019. "Effect of the fractional foundation on the response of beam structure submitted to moving and wind loads," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 178-188.
  14. González-Calderón, Alfredo & Vivas-Cruz, Luis X. & Taneco-Hernández, M.A. & Gómez-Aguilar, J.F., 2023. "Assessment of the performance of the hyperbolic-NILT method to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 375-390.
  15. Xing, Sheng Yan & Lu, Jun Guo, 2009. "Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1163-1169.
  16. Songshu Liu, 2022. "Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
  17. Ning, Xin & Ma, Yanyan & Li, Shuai & Zhang, Jingmin & Li, Yifei, 2018. "Response of non-linear oscillator driven by fractional derivative term under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 102-107.
  18. Ali, Farhad & Iftikhar, Muhammad & Khan, Ilyas & Sheikh, Nadeem Ahmad, 2019. "Atangana–Baleanu fractional model for electro-osmotic flow of viscoelastic fluids," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 125-133.
  19. Ngounou, A.M. & Mba Feulefack, S.C. & Anague Tabejieu, L.M. & Nana Nbendjo, B.R., 2022. "Design, analysis and horseshoes chaos control on tension leg platform system with fractional nonlinear viscoelastic tendon force under regular sea wave excitation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
  20. André Liemert & Alwin Kienle, 2016. "Fractional Schrödinger Equation in the Presence of the Linear Potential," Mathematics, MDPI, vol. 4(2), pages 1-14, May.
  21. Li, Wei & Huang, Dongmei & Zhang, Meiting & Trisovic, Natasa & Zhao, Junfeng, 2019. "Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 30-38.
  22. Aitzhanov, S.E. & Kusherbayeva, U.R. & Bekenayeva, K.S., 2022. "Solvability of pseudoparabolic equation with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
  23. Kumar, Devendra & Nama, Hunney & Baleanu, Dumitru, 2024. "Dynamical and computational analysis of fractional order mathematical model for oscillatory chemical reaction in closed vessels," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
  24. Jehad Alzabut & Ravi P. Agarwal & Said R. Grace & Jagan M. Jonnalagadda & A. George Maria Selvam & Chao Wang, 2022. "A Survey on the Oscillation of Solutions for Fractional Difference Equations," Mathematics, MDPI, vol. 10(6), pages 1-28, March.
  25. Bhuvaneswari Sambandham & Aghalaya S. Vatsala, 2015. "Basic Results for Sequential Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 3(1), pages 1-16, March.
  26. Shahram Rezapour & Sotiris K. Ntouyas & Abdelkader Amara & Sina Etemad & Jessada Tariboon, 2021. "Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
  27. Majumdar, Prahlad & Mondal, Bapin & Debnath, Surajit & Ghosh, Uttam, 2022. "Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
  28. Sivaporn Ampun & Panumart Sawangtong, 2021. "The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
  29. Anague Tabejieu, L.M. & Nana Nbendjo, B.R. & Woafo, P., 2016. "On the dynamics of Rayleigh beams resting on fractional-order viscoelastic Pasternak foundations subjected to moving loads," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 39-47.
  30. Maneesha Gupta & Richa Yadav, 2013. "Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts," Journal of Optimization, Hindawi, vol. 2013, pages 1-11, June.
  31. Bhalekar, Sachin & Gupta, Deepa, 2022. "Stability and bifurcation analysis of a fractional order delay differential equation involving cubic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
  32. Gupta, Sandipan & Ranta, Shivani, 2022. "Legendre wavelet based numerical approach for solving a fractional eigenvalue problem," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
  33. Emadifar, Homan & Nonlaopon, Kamsing & Muhammad, Shoaib & Nuruddeen, Rahmatullah Ibrahim & Kim, Hwajoon & Ahmad, Abdulaziz Garba, 2023. "Analytical investigation of the coupled fractional models for immersed spheres and oscillatory pendulums," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
  34. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
  35. Tabatabaei-Nejhad, Seyede Zahra & Eghtesad, Mohammad & Farid, Mehrdad & Bazargan-Lari, Yousef, 2022. "Combination of fractional-order, adaptive second order and non-singular terminal sliding mode controls for dynamical systems with uncertainty and under-actuation property," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
  36. Gao, Mingyuan & Wang, Yuan & Wang, Yifeng & Yao, Ye & Wang, Ping & Sun, Yuhua & Xiao, Jieling, 2020. "Modeling and experimental verification of a fractional damping quad-stable energy harvesting system for use in wireless sensor networks," Energy, Elsevier, vol. 190(C).
  37. Erman, Sertaç & Demir, Ali, 2020. "On the construction and stability analysis of the solution of linear fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
  38. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
  39. Trong, Dang Duc & Hai, Dinh Nguyen Duy & Minh, Nguyen Dang, 2019. "Optimal regularization for an unknown source of space-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 184-206.
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