Large Fractional Linear Type Differential Equations

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DOI: https://doi.org/10.28924/2291-8639-21-2023-65
Published: Jul 10, 2023
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Ma'mon Abu Hammad, Iqbal Jebril, Roshdi Khalil, Large Fractional Linear Type Differential Equations, Int. J. Anal. Appl., 21 (2023), 65.

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Ma'mon Abu Hammad, Iqbal Jebril, Roshdi Khalil

Abstract

This paper aims to handle some types of fractional differential equations with a fractional-order values β>1. In particular, we propose a novel analytical solution called an atomic solution for certain fractional linear type differential equations as well as for some other types of partial differential equations with fractional-order values exceeding one. Some examples are provided to validate our findings.

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References

  1. I.M. Batiha, S. Alshorm, A. Ouannas, S. Momani, O.Y. Ababneh, M. Albdareen, Modified Three-Point Fractional Formulas with Richardson Extrapolation, Mathematics. 10 (2022), 3489. https://doi.org/10.3390/math10193489.
  2. I.M. Batiha, S. Alshorm, I.H. Jebril, M.A. Hammad, A Brief Review about Fractional Calculus, Int. J. Open Probl. Comput. Math. 15 (2022), 39-56.
  3. I.M. Batiha, A. Obeidat, S. Alshorm, A. Alotaibi, H. Alsubaie, S. Momani, M. Albdareen, F. Zouidi, S.M. Eldin, H. Jahanshahi, A Numerical Confirmation of a Fractional-Order COVID-19 Model’s Efficiency, Symmetry. 14 (2022), 2583. https://doi.org/10.3390/sym14122583.
  4. I.M. Batiha, O.Y. Ababneh, A.A. Al-Nana, W.G. Alshanti, S. Alshorm, S. Momani, A Numerical Implementation of Fractional-Order PID Controllers for Autonomous Vehicles, Axioms. 12 (2023), 306. https://doi.org/10.3390/axioms12030306.
  5. I.H. Jebril, I.M. Batiha, On the Stability of Commensurate Fractional-Order Lorenz System, Progr. Fract. Differ. Appl. 8 (2022), 401-407. https://doi.org/10.18576/pfda/080305.
  6. T. Abdeljawad, On Conformable Fractional Calculus, J. Comput. Appl. Math. 279 (2015), 57-66. https://doi.org/10.1016/j.cam.2014.10.016.
  7. M. Adil Khan, Y.M. Chu, A. Kashuri, R. Liko, G. Ali, Conformable Fractional Integrals Versions of HermiteHadamard Inequalities and Their Generalizations, J. Funct. Spaces. 2018 (2018), 6928130. https://doi.org/10.1155/2018/6928130.
  8. R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A New Definition of Fractional Derivative, J. Comput. Appl. Math. 264 (2014), 65-70. https://doi.org/10.1016/j.cam.2014.01.002.
  9. E. Mahmoudi, The Beta Generalized Pareto Distribution With Application to Lifetime Data, Math. Computers Simul. 81 (2011), 2414-2430. https://doi.org/10.1016/j.matcom.2011.03.006.
  10. M.A. Hammad, Conformable Fractional Martingales and Some Convergence Theorems, Mathematics. 10 (2021), 6. https://doi.org/10.3390/math10010006.
  11. M.A. Hammad, M.A. Horani, A. Shmasenh, R. Khalil, Reduction of Order of Fractional Differential Equations, J. Math. Comput. Sci. 8 (2018), 683-688. https://doi.org/10.28919/jmcs/3806.
  12. A. Dababneh, B. Albarmawi, M.A. Hammad, A. Zraiqat, T. Hamadneh, Conformable Fractional Bernoulli Differential Equation with Applications, in: 2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology (JEEIT), IEEE, Amman, Jordan, 2019: pp. 421-424. https://doi.org/10.1109/JEEIT.2019.8717456.
  13. W.S. Chung, Fractional Newton Mechanics With Conformable Fractional Derivative, J. Comput. Appl. Math. 290 (2015), 150-158. https://doi.org/10.1016/j.cam.2015.04.049.
  14. M. Horani, M.A. Hammad, R. Khalil, Variation of Parameters for Local Fractional Nonhomogenous LinearDifferential Equations, J. Math. Computer Sci. 16 (2016), 147-153.
  15. W. Deeb, R. Khalil, Best approximation in L(X, Y ), Math. Proc. Camb. Phil. Soc. 104 (1988), 527-531. https://doi.org/10.1017/s0305004100065713.
  16. M.A. Hammad, R. Khalil, Fractional Fourier Series With Applications, Amer. J. Comput. Appl. Math. 4 (2014), 187-191.
  17. M. Al-Horani, R. Khalil, I. Aldarawi, Fractional Cauchy Euler Differential Equation, J. Comput. Anal. Appl. 28 (2020), 226-233.
  18. R. Khalil, Isometries of Lp∗ a ⊗ Lp, Tam. J. Math. 16 (1985), 77-85.
  19. H. Al-Zoubi, A. Dabaneh, M. Al-Sabbagh, Ruled Surfaces of Finite II-Type, WSEAS Trans. Math. 18 (2019), 1-5.
  20. F. Bekraoui, M. Al-Horani, R. Khalil, Atomic Solution of Fractional Abstract Cauchy Problem of High Order in Banach Spaces, Eur. J. Pure Appl. Math. 15 (2022), 106-125.