A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation
Abstract
:1. Introduction
2. Preliminaries Results
- ;
- ;
- , for any ;
- ;
- (1)
- (2)
3. Construction of MFS-ASs via Laplace FPSM
- ▪
- , and for , and .
- ▪
- , and for , and .
- ▪
- , and , for , , and .
4. Numerical Experiments
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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1.105171 | 1.105171 | |||
0.818731 | 0.818731 | |||
0.606531 | 0.606531 | |||
0.449329 | 0.449329 | |||
0.332871 | 0.332874 | |||
0.246597 | 0.246618 | |||
0.496585 | 0.496585 | |||
0.367879 | 0.367879 | |||
0.272532 | 0.272532 | |||
0.201897 | 0.201897 | |||
0.149569 | 0.14957 | |||
0.110803 | 0.110813 |
6th-MFS Solutions | |||||||
---|---|---|---|---|---|---|---|
0.1 | 0.904837 | 0.904837 | 0.880178 | 0.825680 | 0.765968 | ||
0.3 | 0.606536 | 0.606531 | 0.583764 | 0.543398 | 0.515907 | ||
0.5 | 0.406764 | 0.406570 | 0.398782 | 0.398511 | 0.466931 | ||
0.7 | 0.274494 | 0.272532 | 0.286770 | 0.371405 | 0.745565 | ||
0.9 | 0.193599 | 0.182684 | 0.245210 | 0.556451 | 1.740233 | ||
0.1 | 0.740818 | 0.740818 | 0.720628 | 0.676004 | 0.627092 | ||
0.3 | 0.496590 | 0.496585 | 0.477923 | 0.444708 | 0.421253 | ||
0.5 | 0.333030 | 0.332871 | 0.326319 | 0.324557 | 0.371555 | ||
0.7 | 0.224737 | 0.223130 | 0.233829 | 0.294632 | 0.558375 | ||
0.9 | 0.158505 | 0.149569 | 0.196769 | 0.419641 | 1.253198 |
Laplace FPSM | NDM [20] | ||||
---|---|---|---|---|---|
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Alaroud, M.; Alomari, A.-K.; Tahat, N.; Al-Omari, S.; Ishak, A. A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation. Mathematics 2023, 11, 2181. https://doi.org/10.3390/math11092181
Alaroud M, Alomari A-K, Tahat N, Al-Omari S, Ishak A. A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation. Mathematics. 2023; 11(9):2181. https://doi.org/10.3390/math11092181
Chicago/Turabian StyleAlaroud, Mohammad, Abedel-Karrem Alomari, Nedal Tahat, Shrideh Al-Omari, and Anuar Ishak. 2023. "A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation" Mathematics 11, no. 9: 2181. https://doi.org/10.3390/math11092181
APA StyleAlaroud, M., Alomari, A.-K., Tahat, N., Al-Omari, S., & Ishak, A. (2023). A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation. Mathematics, 11(9), 2181. https://doi.org/10.3390/math11092181