Browsing by Author "Carmenate, Hector"
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Publication A generalized bernoulli differential equation(2025) Carmenate, Hector; Bosch, Paul; Nápoles, Juan; Sigarreta, JoséIn this paper we study a generalized form of the Bernoulli Differential Equation, employing a generalized conformable derivative. Initially, we establish a generalized variant of Gronwall’s inequality, essential for assessing the stability of generalized differential equation systems, and offer insights into the qualitative behavior of the trivial solution of the proposed equation. Subsequently, we present and prove the main results concerning the solution of the generalized Bernoulli Differential Equation, complemented by illustrative examples that underscore the advantages of this generalized derivative approach. Furthermore, we introduce a finite difference method as an alternative technique to approximate the solution of the generalized Bernoulli equation and demonstrate its validity through practical examples.