Analytical Solutions for a Generalized Nonlinear Local Fractional Bratu-Type Equation in a Fractal Environment
Abstract
:1. Introduction
2. Preliminaries
2.1. Local Fractal Derivative
2.2. Local Fractal Integral
2.3. Properties of Local Fractional Derivatives
- (i)
- (ii)
- (iii)
2.4. Mittag-Leffler Function
3. Adomian Decomposition Method (ADM)
4. Solution of Generalized Local Fractional Bratu Equation
5. Particular Cases
- Special Case (i):
- Special Case (ii):
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
time co-ordinate | |
space co-ordinate | |
constant | |
℘ | constant |
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Alhamzi, G.; Dubey, R.S.; Alkahtani, B.S.T.; Saini, G.L. Analytical Solutions for a Generalized Nonlinear Local Fractional Bratu-Type Equation in a Fractal Environment. Fractal Fract. 2024, 8, 15. https://doi.org/10.3390/fractalfract8010015
Alhamzi G, Dubey RS, Alkahtani BST, Saini GL. Analytical Solutions for a Generalized Nonlinear Local Fractional Bratu-Type Equation in a Fractal Environment. Fractal and Fractional. 2024; 8(1):15. https://doi.org/10.3390/fractalfract8010015
Chicago/Turabian StyleAlhamzi, Ghaliah, Ravi Shanker Dubey, Badr Saad T. Alkahtani, and G. L. Saini. 2024. "Analytical Solutions for a Generalized Nonlinear Local Fractional Bratu-Type Equation in a Fractal Environment" Fractal and Fractional 8, no. 1: 15. https://doi.org/10.3390/fractalfract8010015
APA StyleAlhamzi, G., Dubey, R. S., Alkahtani, B. S. T., & Saini, G. L. (2024). Analytical Solutions for a Generalized Nonlinear Local Fractional Bratu-Type Equation in a Fractal Environment. Fractal and Fractional, 8(1), 15. https://doi.org/10.3390/fractalfract8010015