Organization profile
Organization profile
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.
UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. Our work contributes towards the following SDG(s):
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SDG 3 Good Health and Well-being -
SDG 4 Quality Education -
SDG 6 Clean Water and Sanitation -
SDG 7 Affordable and Clean Energy -
SDG 9 Industry, Innovation, and Infrastructure -
SDG 10 Reduced Inequalities
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Collaborations and top research areas from the last five years
Profiles
Research output
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ABUNDANT SOLITONS SOLUTIONS OF THE (2+1)-DIMENSIONAL KADOMTSEVPETVIASHVILI-MODIFIED EQUAL WIDTH MODEL
Shafique, T., Agarwal, R. P., Mohammed, P. O., Abbas, M., Vivas-Cortez, M., Nazir, T. & Djaouti, A. M., 2026, In: Fractals. 34, 4, 2540133.Research output: Contribution to journal › Article › peer-review
Open Access2 Link opens in a new tab Scopus citations -
Existence and stability of a mild solution to an abstract sequential time-fractional diffusion equation of pantograph type
Melha, K. O., Thabet, S. T. M., Djaouti, A. M., Kedim, I., Aldwoah, K. & Vivas-Cortez, M., 2026, In: Journal of Mathematics and Computer Science. 41, 3, p. 421-436 16 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Una variación de la Transformada Doble de Laplace No-Conformable
Translated title of the contribution :A variation of the Non-Conformable Double Laplace Transform Research output: Contribution to journal › Article › peer-review
Open Access
Projects
- 2 Active
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Contemporary Theoretical Challenges and Practical Advances in Fractional and Generalized Calculus
Vivas Cortez, M. J. (Di), Guerrero, J. A. (External), Juan E., N. V. (External) & Velasco Velasco, J. (PI)
30/07/25 → 1/08/27
Project: Research project
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LA DERIVADA FRACCIONAL GENERALIZADA, NUEVOS RESULTADOS Y APLICACIONES EN DESIGUALDADES INTEGRALES
Vivas Cortez, M. J. (Di), Jaramillo Villagómez, J. E. (PI), VELASCO VELASCO, J. (External), Thabet, S. T. M. (External) & BRAVO QUEZADA, W. G. (PI)
10/08/24 → 11/08/26
Project: Research project
Activities
- 3 Invited talk
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A New Generalized Local Derivative of Two Parameters
Vivas Cortez, M. J. (Speaker)
2025Activity: Talk types › Invited talk
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Algunos resultados sobre derivadas fraccionarias y generalizadas
Vivas Cortez, M. J. (Speaker)
13 Nov 2024 → 15 Nov 2024Activity: Talk types › Invited talk
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XX Encuentro Internacional de Matemáticas
Vivas Cortez, M. J. (Speaker)
2024Activity: Talk types › Invited talk