A Novel Approach for Solving Fractional Differential Equations via a Multistage Telescoping Decomposition Method
Abstract
1. Introduction and Mathematical Preliminaries
2. Fundamental Definitions
2.1. Fractional Calculus
2.2. Properties and Definition of Elzaki Transform
2.3. Algorithm of Telescoping Decomposition Method
Multistage Telescoping Decomposition Method
3. Multistage Telescoping Decomposition Elzaki Method
3.1. Solving the Nonlinear Fractional Differential Equations
3.2. Solving the Nonlinear Fractional Partial Differential Equations
4. Program of the MFTDM
Algorithm 1: Programme of the novel algorithm. |
Programme: ; endproc: Warning, ’g’ is implicitly declared local to procedure ’abc’ >for k from 2 to n do ; end; >for i from 1 to do >for k from 2 to n do ; print end; |
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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1 | |||
ADM Error | FTDM Error | MFTDEM 1 Error | MFTDEM 2 | |
---|---|---|---|---|
0 | 0 | 0 | 0 | 0 |
0.5 | 0.0000527183 | 0.0000138244 | 0.000258833 | 0.000014334 |
1 | 4.11264 | 0.0044278890 | 0.00392701 | 0.000198 |
1.5 | 10323.1 | 0.09144481177 | 0.0062466 | 0.00023656 |
2 | 0.5723355101 | 0.00493943 | 0.00021433 | |
2.5 | 1.075212598 | 0.00285709 | 0.00060915 | |
3 | 7.413059554 | 0.00141436 | 0.000064128 | |
3.5 | 304.3789789 | 0.00524319 | 0.00019047 | |
4 | 4250.670072 | 0.0213869 | 0.0022778 | |
4.5 | 35669.87361 | 0.0587671 | 0.0099358 | |
5 | 861.079 | 0.126514 | 0.027505 | |
5.5 | 1796.48 | 0.23312 | 0.059500 | |
6 | 3473.63 | 0.385885 | 0.11034 |
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Chita, F.; Ayadi, S.; Erden Ege, M.; Ege, O.; Ramaswamy, R. A Novel Approach for Solving Fractional Differential Equations via a Multistage Telescoping Decomposition Method. Fractal Fract. 2025, 9, 65. https://doi.org/10.3390/fractalfract9020065
Chita F, Ayadi S, Erden Ege M, Ege O, Ramaswamy R. A Novel Approach for Solving Fractional Differential Equations via a Multistage Telescoping Decomposition Method. Fractal and Fractional. 2025; 9(2):65. https://doi.org/10.3390/fractalfract9020065
Chicago/Turabian StyleChita, Fouzia, Souad Ayadi, Meltem Erden Ege, Ozgur Ege, and Rajagopalan Ramaswamy. 2025. "A Novel Approach for Solving Fractional Differential Equations via a Multistage Telescoping Decomposition Method" Fractal and Fractional 9, no. 2: 65. https://doi.org/10.3390/fractalfract9020065
APA StyleChita, F., Ayadi, S., Erden Ege, M., Ege, O., & Ramaswamy, R. (2025). A Novel Approach for Solving Fractional Differential Equations via a Multistage Telescoping Decomposition Method. Fractal and Fractional, 9(2), 65. https://doi.org/10.3390/fractalfract9020065