Solution of fractional autonomous ordinary differential equations
Volume 27, Issue 1, pp 59--64
http://dx.doi.org/10.22436/jmcs.027.01.05
Publication Date: February 10, 2022
Submission Date: November 03, 2021
Revision Date: November 25, 2021
Accteptance Date: January 01, 2022
-
1247
Downloads
-
2832
Views
Authors
R. AlAhmad
- Mathematics department, Yarmouk University, Irbid, 21163, Jordan.
- Department of Mathematics and Natural Sciences, Higher colleges of technology, Ras AlKhaimah, UAE.
Q. AlAhmad
- Mathematics Department, California state university at Northridge, Northridge, CA 91330-8313, USA.
A. Abdelhadi
- Department of Mathematics and Natural Sciences, Higher colleges of technology, Ras AlKhaimah, UAE.
Abstract
Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.
Share and Cite
ISRP Style
R. AlAhmad, Q. AlAhmad, A. Abdelhadi, Solution of fractional autonomous ordinary differential equations, Journal of Mathematics and Computer Science, 27 (2022), no. 1, 59--64
AMA Style
AlAhmad R., AlAhmad Q., Abdelhadi A., Solution of fractional autonomous ordinary differential equations. J Math Comput SCI-JM. (2022); 27(1):59--64
Chicago/Turabian Style
AlAhmad, R., AlAhmad, Q., Abdelhadi, A.. "Solution of fractional autonomous ordinary differential equations." Journal of Mathematics and Computer Science, 27, no. 1 (2022): 59--64
Keywords
- Fractional derivatives
- Caputo fractional derivative
- the Caputo-Fabrizio fractional derivative
- Laplace transform
MSC
References
-
[1]
R. AlAhmad, Products of incomplete gamma functions, Analysis (Berlin), 36 (2016), 199--203
-
[2]
R. AlAhmad, Products of Incomplete gamma functions Integral representations, Math. Sci. Appl. E-Notes, 4 (2016), 47--51
-
[3]
R. AlAhmad, Laplace transform of the product of two functions, Ital. J. Pure Appl. Math., 2020 (2020), 800--804
-
[4]
R. AlAhmad, M. Al-Jararha, On solving some classes of second order ODEs, Italian J. Pure Appl. Math., 45 (2021), 673--688
-
[5]
. AlAhmad, M. Al-Jararha, H. AlMefleh, Exactness of second order ordinary differential equations and integrating factors, Jordan J. Math. Stat., 11 (2015), 155--167
-
[6]
S. Al-Ahmad, N. Anakira, M. Mamat, I. M. Suliman, R. AlAhmad, Modified differential transformation scheme for solving classes of non-linear differential equations, TWMS J. Appl. Eng. Math., (Accepted)
-
[7]
S. Al-Ahmad, M. Mamat, R. Al-Ahmad, Finding Differential Transform Using Difference Equations, IAENG Int. J. Appl. Math., 50 (2020), 127--132
-
[8]
S. Al-Ahmad, M. Mamat, R. Al-Ahmad, I. M. Sulaiman, P. L. Ghazali, M. A. Mohamed, On New Properties of Differential Transform via Difference Equations, Int. J. Eng. Tech., 7 (2018), 321--324
-
[9]
R. AlAhmad, R. Weikard, On inverse problems for left-definite discrete Sturm-Liouville equations, Oper. Matrices, 7 (2013), 35--70
-
[10]
M. Caputo, M. Fabrizio, On the singular kernels for fractional derivatives. some applications to partial differential equations, Progr. Fract. Differ. Appl., 7 (2021), 79--82
-
[11]
Y. L. Chen, F. W. Liu, Q. Yu, T. Z. Li, Review of fractional epidemic models, Appl. Math. Model., 97 (2021), 281--307
-
[12]
R. K. Gazizov, S. Y. Lukashchuk, Higher-order symmetries of a time-fractional anomalous diffusion equation, Mathematics, 9 (2021), 11 pages
-
[13]
C. Ionescu, A. Lopes, D. Copot, J. A. T. Machado, J. H. T. Bates, The role of fractional calculus in modeling biological phenomena: a review, Commun. Nonlinear Sci. Numer. Simul., 51 (2017), 141--159
-
[14]
C. I. Muresan, I. R. Birs, E. H. Dulf, D. Copot, L. Miclea, A review of recent advances in fractional-order sensing and filtering techniques, Sensors, 21 (2021), 281--307
-
[15]
J. J. Nieto, Solution of a fractional logistic ordinary differential equation, Appl. Math. Lett., 123 (2022), 5 pages
-
[16]
H. R. Thieme, Mathematics in Population Biology, Princeton University Press, Princeton (2018)