Generalization of the Nonlinear Bernoulli Conformable Fractional Differential Equations with Applications

In this work, we study a well-known nonlinear fractional differential equation—the nonlinear Bernoulli conformable fractional differential equation. We classify this equation into different categories and establish a fundamental lemma essential for proving our generalization. This generalization incorporates two methods: the Conformable Leibniz Method and the Conformable Bernoulli Method, both of which provide exact solutions for any nonlinear Bernoulli equation. Finally, we demonstrate the effectiveness of our approach by applying it to selected nonlinear Bernoulli conformable fractional differential equations, including a detailed numerical example.