10.57647/j.jtap.2025.1904.41

Exact solutions to the Bernoulli and Riccati equations with conformable derivatives: An application to liquid flow in reservoirs, tanks, and funnels

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  • Mustafa Aydin*1,
  1. Department of Medical Services and Techniques, Muradiye Vocational School, Van Yuzuncu Yil University, Van, Turkey

Received: 2025-02-24

Revised: 2025-08-06

Accepted: 2025-08-18

Published in Issue 2025-08-31

Copyright (c) 2025 Mustafa Aydin (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
Aydin M. Exact solutions to the Bernoulli and Riccati equations with conformable derivatives: An application to liquid flow in reservoirs, tanks, and funnels. J Theor Appl phys. 2025 Aug. 31;19(4). Available from: https://oiccpress.com/jtap/article/view/17663
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Abstract

This study presents an explicit representation of the solution for a linear conformable differential system with variable coefficients,  utilizing the method of variation of constants combined with the state-transition approach. To tackle the exact solutions of nonlinear fractional Bernoulli-type and Riccati-type differential equations involving conformable derivatives-as well as separable fractional  differential equations-these are skillfully transformed into an equivalent linear conformable system through appropriate variable substitutions. Theoretical results are further substantiated by detailed numerical and simulated examples. Moreover, the practical applicability of the proposed method is demonstrated through modeling liquid flow in engineering structures such as reservoirs, tanks, and funnels.

Keywords

  • Conformable fractional derivative,
  • Riccati type differential equation,
  • Bernoulli type differential equation;,
  • Representation of solutions,
  • State-transition operator
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