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The research aims to establish existence, uniqueness, and continuous dependence of solutions for deformable derivative initial value problems.

March 28, 2026Open Access

Existence, Uniqueness and Continuous Dependence for Deformable Derivative Initial Value Problems

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The research aims to establish existence, uniqueness, and continuous dependence of solutions for deformable derivative initial value problems.
Developed a theoretical framework for analyzing deformable derivative problems.
Proved local existence and uniqueness using the Banach fixed-point theorem under Lipschitz continuity.
Extended results to global existence under linear growth conditions.
Demonstrated continuous dependence on initial conditions and parameters.
Generalized the theory to systems of equations.
Established local existence and uniqueness of solutions for deformable derivatives.
Proved global existence under specific conditions.
Showed continuous dependence on initial conditions.
Confirmed the applicability of deformable derivatives in modeling complex systems.

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Theoretical framework establishes local and global solution existence in deformable derivative problems, suggesting a new modeling tool.

Priya et al. (2025) studied this question.

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