Exact solutions of some fractal differential equations

In this paper, we explore the intriguing field of fractal calculus as it pertains to fractal curves and fractal sets. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for solving α-order differential equations. Notably, we extend...

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Bibliographic Details
Published in:Applied mathematics and computation 2024-07, Vol.472, p.128633, Article 128633
Main Authors: Khalili Golmankhaneh, Alireza, Bongiorno, Donatella
Format: Article
Language:English
Subjects:
Fractal calculus
Fractal curves
Fractal differential equations
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Summary:In this paper, we explore the intriguing field of fractal calculus as it pertains to fractal curves and fractal sets. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for solving α-order differential equations. Notably, we extend our analysis to solve Fractal Bernoulli differential equations. The applications of our findings are then showcased through the solutions of problems such as fractal compound interest and the escape velocity of the earth in fractal space and time. Visual representations of our results are also provided to enhance understanding. •The fractal separable method and the integrating factor technique are suggested.•Fractal Bernoulli differential equations are given and solved.•The escape velocity of the earth in fractal space and time is studied.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2024.128633