The FRACTAL group is dedicated to the advanced study of fractional differential equation theory, nonlinear analysis, and generalized convexity. We seek to develop and apply theoretical and numerical tools to address complex problems in these fields. Key objectives include:

• Developing and applying innovative methods in solving nonlinear fractional equations, extending classical results to more general and complex contexts.
• Establishing new theoretical connections between nonlinear analysis, generalized convexity, and fractional variations to explore fundamental properties of functions, their stability, and existence of solutions.
• Designing practical applications that utilize these theoretical frameworks to model physical, biological, and economic phenomena, with a focus on nonlinear dynamic systems and their control.
• Promoting the use of advanced numerical techniques for simulation and solution of fractional and nonlinear models, allowing for approximate solutions in real-world contexts.
• Collaborating internationally with other research centers, expanding the theoretical and applied base of nonlinear analysis and differential equations in interdisciplinary contexts.