Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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TAYLORS SERIES IN TERMS OF THE MODIFIED CONFORMABLE FRACTIONAL DERIVATIVE WITH APPLICATIONS

  • Mohammed B. M. Altalla (Department of Mathematics, PET Research Foundation, University of Mysore) ;
  • B. Shanmukha (Department of Mathematics, PES College of Engineering) ;
  • Ahmad El-Ajou (Department of Mathematics, Faculty of Science, Al Balqa Applied University) ;
  • Mohammed N. A. Alkord (Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University)
  • Received : 2023.08.08
  • Accepted : 2023.12.23
  • Published : 2024.06.15
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Abstract

This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations.

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References

  1. T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66, doi.org/10.5923/j.ajcam.20140406.01. 
  2. I. Abu Hammad and R. Khalil, Fractional Fourier series with applications, Amer. J. Comput. Appl. Math., 4(6) (2014), 187-191, doi.org/10.5923/j.ajcam.20140406.01. 
  3. A. T. Alabdala, B. N. Abood, S. S. Redhwan and S. Alkhatib, Caputo delayed fractional differential equations by Sadik transform, Nonlinear Funct. Anal. Appl., 28(2) (2023), 439-448. 
  4. A. El-Ajou, A modification to the conformable fractional calculus with some applications, Alexandria Eng. J., 59(4) (2020), 2239-2249, doi.org/10.1016/j.aej.2020.02.003. 
  5. A. El-Ajou, O.A. Arqub, Z.A. Zhour and S. Momani, New results on fractional power series: theories and applications, Entropy, 15(12) (2013), 5305-5323, doi.org/10.3390/e15125305. 
  6. F.M. Gonzalez, I. Martinez Vidal, M. Kaabar and S. Paredes, Some new results on conformable fractional power series, Asia Pacific J. Math., 7(31) (2020), 1-14, doi.org/10.28924/APJM/7-31. 
  7. F. M. Ismaael, An investigation on the existence and uniqueness analysis of the fractional nonlinear integro-differential equations, Nonlinear Funct. Anal. Appl., 28(1) (2023), 237-249 
  8. R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70, doi.org/10.1016/j.cam.2014.01.002. 
  9. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of the Fractional Differential Equations, 204 North-Holland Mathematics Studies, Elsevier, Amsterdam, 2006. 
  10. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993. 
  11. Z.M. Odibat and N.T. Shawagfeh, Generalized Taylors formula, Appl. Math. Comput., 186(1) (2007), 286-293, doi.org/10.1016/j.amc.2006.07.102. 
  12. K. Oldham and J. Spanier, The Fractional Calculus, Theory and Applications of Differentiation and Integration of Arbitrary Order, Academic Press, USA, 1974. 
  13. I. Podlubny, Fractional Differential Equations, Academic Press, USA, 1999. 
  14. S.T. Syouri, M. Mamat, I.M. Alghrouz and I.M. Sulaiman, Conformable fractional differintegral method for solving fractional equations, AQU Researchers Publications, 2020, https://dspace.alquds.edu/handle/20.500.12213/5684. 
  15. J.J. Trujillo, M. Rivero and B. Bonilla, On a RiemannLiouville generalized Taylor's formula, J. Math. Anal. Appl., 231(1) (1999), 255-265, doi.org/10.1006/jmaa.1998.6224. 
  16. E. Unal and A. Gokdogan, Solution of conformable fractional ordinary differential equations via differential transform method, Optik-Int. J. Light Electron Opt, 128 (2017), 264-273, doi.org/10.1016/j.ijleo.2016.10.031.