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Exact solutions of some fractal differential equations

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  • Khalili Golmankhaneh, Alireza
  • Bongiorno, Donatella

Abstract

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.

Suggested Citation

  • Khalili Golmankhaneh, Alireza & Bongiorno, Donatella, 2024. "Exact solutions of some fractal differential equations," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    • Handle: RePEc:eee:apmaco:v:472:y:2024:i:c:s009630032400105x
    DOI: 10.1016/j.amc.2024.128633
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    References listed on IDEAS

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    1. Balankin, Alexander S. & Mena, Baltasar, 2023. "Vector differential operators in a fractional dimensional space, on fractals, and in fractal continua," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Golmankhaneh, Alireza K. & Tunç, Cemil, 2019. "Sumudu transform in fractal calculus," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 386-401.
    3. Khalili Golmankhaneh, Alireza & Tejado, Inés & Sevli, Hamdullah & Valdés, Juan E. Nápoles, 2023. "On initial value problems of fractal delay equations," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    4. Babak Shiri & Zahra Alijani & Yeliz Karaca, 2023. "A Power Series Method For The Fuzzy Fractional Logistic Differential Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-11.
    5. El-Nabulsi, Rami Ahmad & Khalili Golmankhaneh, Alireza & Agarwal, Praveen, 2022. "On a new generalized local fractal derivative operator," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Shiri, Babak & Baleanu, Dumitru, 2023. "All linear fractional derivatives with power functions’ convolution kernel and interpolation properties," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Balankin, Alexander S. & Ramírez-Joachin, Juan & González-López, Gabriela & Gutíerrez-Hernández, Sebastián, 2022. "Formation factors for a class of deterministic models of pre-fractal pore-fracture networks," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
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    Cited by:

    1. Qin, Bo & Zhang, Ying, 2024. "Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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