Alqahtani Hagag 2023b - Revision history

Rimni: /* References */

2023-10-25T13:02:18Z

‎References

Ahmedshehata at 12:49, 25 October 2023

2023-10-25T12:49:25Z

Ahmedshehata at 12:46, 25 October 2023

2023-10-25T12:46:17Z

Rimni at 12:18, 24 October 2023

2023-10-24T12:18:12Z

Rimni at 14:24, 23 October 2023

2023-10-23T14:24:25Z

Rimni at 14:15, 23 October 2023

2023-10-23T14:15:32Z

Rimni at 14:05, 23 October 2023

2023-10-23T14:05:02Z

Rimni: /* 7 Conclusion */

2023-10-23T13:29:33Z

‎7 Conclusion

Show changes

Rimni at 11:55, 23 October 2023

2023-10-23T11:55:39Z

Rimni: /* Application 3 */

2023-10-23T11:42:20Z

‎Application 3

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 <div id="cite-25"></div>
-[25] Alqahtani Z, Hagag AE. A fractional numerical study on a plant disease model with replanting and preventive treatment. Métodos numéricos para cálculo y diseño en ingeniería: Revista internacional, 39(3):1-21, 2023.
+[25] Alqahtani Z, Hagag AE. A fractional numerical study on a plant disease model with replanting and preventive treatment. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 39(3), 27, 2023.
 <div id="cite-26"></div>

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 respectively.
-Long-wave propagation in nonlinear media with dispersion and dissipation is modeled using Eq. ([[#eq-1|1]]) [16]. Using both an automated technique and the homogeneous balancing technique, a kind solution to Eq. ([[#eq-1|1]]) has been discovered [18–19]. A type of Backlund transformation for this system has recently been developed [20]. In the one-dimensional nonlinear lattice [16], the wave propagation of limited particles with a harmonic force may be described by Eq. (2) [17]. In particular, it explains how small-amplitude ion-acoustic waves propagate in plasmas without Landau damping, and it is also used to explain how thermal pulses move through a single crystal of sodium fluoride in solid physics [21-22]. Many studies have been done on this equation.
+Long-wave propagation in nonlinear media with dispersion and dissipation is modeled using Eq. ([[#eq-1|1]]) [16]. Using both an automated technique and the homogeneous balancing technique, a kind solution to Eq. ([[#eq-1|1]]) has been discovered [18–19]. A type of Backlund transformation for this system has recently been developed [20]. In the one-dimensional nonlinear lattice [16], the wave propagation of limited particles with a harmonic force may be described by Eq. (2) [17]. In particular, it explains how small-amplitude ion-acoustic waves propagate in plasmas without Landau damping, and it is also used to explain how thermal pulses move through a single crystal of sodium fluoride in solid physics [21-22]. Many studies have been done on this equation [23-25].
 ==2. Preliminaries to FC==

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 <div id="cite-25"></div>
-[25]
+[25] Alqahtani Z, Hagag AE. A fractional numerical study on a plant disease model with replanting and preventive treatment. Métodos numéricos para cálculo y diseño en ingeniería: Revista internacional, 39(3):1-21, 2023.
 <div id="cite-26"></div>

← Older revision		Revision as of 12:18, 24 October 2023
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	==References==		==References==
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	<div id="cite-1"></div>		<div id="cite-1"></div>

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 <div id="cite-1"></div>
-[1] He, J. A tutorial review on fractal spacetime and fractional calculus. International Journal of Theoretical Physics, 53:3698-3718, 2014.
+[1] He J.H. A tutorial review on fractal spacetime and fractional calculus. International Journal of Theoretical Physics, 53:3698-3718, 2014.
 <div id="cite-2"></div>
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 [29]  Kreyszig E. Introductory functional analysis with applications. Chapter 5: Further applications: Banach fixed point theorems. New York, Wiley Classic Libraries, 299-321, 1989.
 ==Acknowledgments==

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 |}
-The formula for the Laplace transform of the Caputo fractional derivative is [[[#7 Conclusion|7]]]
+The formula for the Laplace transform of the Caputo fractional derivative is [7]
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← Older revision		Revision as of 14:05, 23 October 2023
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	'''Data Availability:''' No data were used to support this study.		'''Data Availability:''' No data were used to support this study.
		+
		+	==Acknowledgments==
		+
		+	This research project was funded by the Deanship of Scientific Research, Princess Nourah bint Abdulrahman University, through the Program of Research Project Funding After Publication, grant No (43- PRFA-P-48).
		+
		+	==References==
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		+	[1] He, J. A tutorial review on fractal spacetime and fractional calculus. International Journal of Theoretical Physics, 53:3698-3718, 2014.
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		+	[7] Podlubny I. Fractional differential equations. Academic Press, New York, pp. 340, 1999.
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	==Acknowledgments==		==Acknowledgments==

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