Large Fractional Linear Type Differential Equations

Hammad, Ma'mon Abu; Jebril, Iqbal; Khalil, Roshdi

doi:10.28924/2291-8639-21-2023-65

Research Article

Large Fractional Linear Type Differential Equations

Ma'mon Abu Hammad
Iqbal Jebril¹*
Roshdi Khalil

a:1:{s:5:"en_US";s:81:"Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11942, Jordan";}

* Corresponding author

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.

How to Cite

M. A. Hammad, I. Jebril, R. Khalil, Large Fractional Linear Type Differential Equations, Int. J. Anal. Appl. 21 (2023), 65. https://doi.org/10.28924/2291-8639-21-2023-65

BibTeX

@article{Hammad2023,
  author  = {Hammad, Ma'mon Abu and Jebril, Iqbal and Khalil, Roshdi},
  title   = {Large Fractional Linear Type Differential Equations},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {65},
  doi     = {10.28924/2291-8639-21-2023-65}
}

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.