MV

Miguel Vivas-Cortez

Also known as: Miguel Vivas, Miguel J. Vivas C., M. Vivas, Miguel José Vivas Cortez, Cortez, M V, Miguel J. Vivas-Cortez

Pontificia Universidad Católica del Ecuador, Escuela Superior Politecnica del Litoral, Universidad Central de Venezuela, Universidad Centroccidental Lisandro Alvarado, Arturo Prat University

Research areas: Mathematics · Applied Mathematics · Mathematical Inequalities and Applications · Approximation Theory and Sequence Spaces · Fractional Differential Equations Solutions

ORCID iD 0000-0002-1567-0264
Follow

About

Dr. Miguel José Vivas-Cortez is a Full Professor of Mathematics at the Pontifical Catholic University of Ecuador (PUCE), Quito, with over 27 years of experience in teaching and mathematical research at undergraduate, master's, and doctoral levels. He holds a degree in Mathematics and a Master's degree in Pure Mathematics from Universidad Centroccidental Lisandro Alvarado (UCLA, Venezuela), and a Ph.D. in Mathematical Sciences. His master's thesis was published in Nonlinear Analysis: Real World Applications (Elsevier, Q1 Scopus).
He is ranked #1 among mathematicians in Ecuador and #6 in Latin America (2019–2025) in mathematical productivity according to SciVal Scopus, and among the top 100 most productive mathematicians globally (2018–2023) in the field of analysis. He is founder and leader of the research group FRACTAL (Fractional Research in Analysis, Convexity and Their Applications) at PUCE.
His research career spans four clearly defined stages:
Stage 1 — Delay Differential Equations in Ecological Models: Early research focused on retarded functional differential equations and their applications to population dynamics and ecological systems, including stability analysis and qualitative behavior of solutions.
Stage 2 — Functional Analysis and Generalized Bounded Variation: Study of functions of generalized bounded variation (in the sense of Jordan, Wiener, Young, Waterman, and Schramm) defined on subsets of the complex plane, with contributions to function space theory and operator-theoretic methods.
Stage 3 — Integral Inequalities and Generalized Convexity: Development of new integral inequalities of Hermite-Hadamard, Ostrowski, Fejer, Simpson, Newton, and Trapezoid type for generalized convex functions, including (h,m)-convex, s-convex, strongly convex, harmonically convex, preinvex, and coordinated convex functions.
Stage 4 — Local and Memory Operators / Fractional Calculus: Research on fractional integral and differential operators including Riemann-Liouville, Caputo, Hadamard, Katugampola, Atangana-Baleanu, conformable, and fractal-fractional operators, with applications to real-world mathematical models in engineering and biology.
Dr. Vivas-Cortez has published extensively in high-impact journals including Scientific Reports (Nature Portfolio), Numerical Algorithms (Springer), Nonlinear Analysis: Real World Applications (Elsevier), Journal of Inequalities and Applications (Springer), Ain Shams Engineering Journal (Elsevier), journals of De Gruyter, Taylor & Francis, and Rendiconti del Circolo Matematico di Palermo (Springer). He has supervised numerous undergraduate, master's, and doctoral theses across all four research areas. 🏆 Ranked in the top 2% of scientists worldwide (Stanford University / Elsevier, 2026 edition) in the field of Mathematics and Statistics, subfield of Applied Mathematics. Ranked 553rd globally in the subfield.
🔗 View: https://topscinet.com/scientist_profile/Vivas-Cortez,%20Miguel/2006/?stype=single_year

Employment

Education

Projects & Funding

Projects & funding information is unavailable.

Publications (291)