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Solution of fractional differential equations by using differential transform method

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  1. Moghaddam, B.P. & Machado, J.A.T. & Behforooz, H., 2017. "An integro quadratic spline approach for a class of variable-order fractional initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 354-360.
  2. Hassan Eltayeb, 2013. "Note on Relation between Double Laplace Transform and Double Differential Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
  3. Skwara, Urszula & Mozyrska, Dorota & Aguiar, Maira & Stollenwerk, Nico, 2024. "Dynamics of vector-borne diseases through the lens of systems incorporating fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
  4. Rehman, Mujeeb ur & Idrees, Amna & Saeed, Umer, 2017. "A quadrature method for numerical solutions of fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 38-49.
  5. Nemati, S. & Lima, P.M., 2018. "Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 79-92.
  6. Ali Ahmadian & Norazak Senu & Farhad Larki & Soheil Salahshour & Mohamed Suleiman & Md. Shabiul Islam, 2013. "Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
  7. İbrahim Avcı & Nazim I. Mahmudov, 2020. "Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
  8. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
  9. Mehmet Merdan & Ahmet Gökdoğan & Ahmet Yıldırım & Syed Tauseef Mohyud-Din, 2012. "Numerical Simulation of Fractional Fornberg‐Whitham Equation by Differential Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
  10. Arikoglu, Aytac & Ozkol, Ibrahim, 2009. "Solution of fractional integro-differential equations by using fractional differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 521-529.
  11. Yongjin Li & Kamal Shah, 2017. "Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
  12. Isaac Addai & Benedict Barnes & Isaac Kwame Dontwi & Kwaku Forkuoh Darkwah, 2025. "The Exact Solutions of the Fractional Partial Differential Equations Using the Fractional Prabhakar Power Series Method," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
  13. Salah Abuasad & Ahmet Yildirim & Ishak Hashim & Samsul Ariffin Abdul Karim & J.F. Gómez-Aguilar, 2019. "Fractional Multi-Step Differential Transformed Method for Approximating a Fractional Stochastic SIS Epidemic Model with Imperfect Vaccination," IJERPH, MDPI, vol. 16(6), pages 1-15, March.
  14. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
  15. Brahim Benhammouda & Hector Vazquez-Leal & Arturo Sarmiento-Reyes, 2014. "Modified Reduced Differential Transform Method for Partial Differential‐Algebraic Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
  16. Damarla, Seshu Kumar & Kundu, Madhusree, 2015. "Numerical solution of multi-order fractional differential equations using generalized triangular function operational matrices," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 189-203.
  17. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
  18. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
  19. Dumitru Baleanu & Mohsen Alipour & Hossein Jafari, 2013. "The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann‐Liouville Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
  20. Süleyman Öğrekçi, 2015. "Generalized Taylor Series Method for Solving Nonlinear Fractional Differential Equations with Modified Riemann‐Liouville Derivative," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
  21. Kumar, Manoj & Daftardar-Gejji, Varsha, 2019. "A new family of predictor-corrector methods for solving fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
  22. Allahviranloo, T. & Gouyandeh, Z. & Armand, A., 2015. "Numerical solutions for fractional differential equations by Tau-Collocation method," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 979-990.
  23. Yu, Jianping & Jing, Jian & Sun, Yongli & Wu, Suping, 2016. "(n+1)-Dimensional reduced differential transform method for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 697-705.
  24. Muhammad Nadeem & Yahya Alsayaad, 2023. "A New Study for the Investigation of Nonlinear Fractional Drinfeld–Sokolov–Wilson Equation," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
  25. Maria Ihsane El Bahi & Khalid Hilal, 2022. "Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV‐Like Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
  26. Yang, Xiao-Jun & Tenreiro Machado, J.A. & Srivastava, H.M., 2016. "A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 143-151.
  27. Wenjin Li & Yanni Pang, 2018. "An Iterative Method for Time‐Fractional Swift‐Hohenberg Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
  28. Shabaz Jalil Mohammedfaeq & Miran Bayan Mohammed Amin & Dashne Chapuk Zahir & Shazad Shawki Ahmed, 2025. "An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
  29. Kavyanpoor, Mobin & Shokrollahi, Saeed, 2017. "Challenge on solutions of fractional Van Der Pol oscillator by using the differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 44-45.
  30. Alam, M. Shamsul & Huq, M. Ashraful & Hasan, M. Kamrul & Rahman, M. Saifur, 2021. "A new technique for solving a class of strongly nonlinear oscillatory equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
  31. Yusuf Pandir & Tolga Akturk & Yusuf Gurefe & Hussain Juya, 2023. "The Modified Exponential Function Method for Beta Time Fractional Biswas‐Arshed Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
  32. Raja, Muhammad Asif Zahoor & Samar, Raza & Manzar, Muhammad Anwar & Shah, Syed Muslim, 2017. "Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 139-158.
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