Fractional Differential Equations

Dr. Praveen Agarwal earned his Ph. D. in Mathematics at the Malviya National Institute of Technology (MNIT) in Jaipur, India, in 2006. Recently, Prof. Agarwal has been listed as the World's Top 2% Scientist from 2020-2025, released by Stanford University. In the 2025 ranking of best scientists worldwide announced by Research.com, he ranked 13th at the India level and 1297th worldwide in Mathematics. Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 24 years. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, Probability & Statistics, and Fixed Point Theorems. He has published 11 research monographs and edited volumes and more than 405 publications (with almost 100 mathematicians all over the world) in prestigious national and international mathematics journals. Dr. Agarwal worked previously either as a regular faculty or as a visiting professor and scientist in universities in several countries, including India, Germany, Turkey, South Korea, UK, Russia, Malaysia and Thailand. He has served over 50 Journals in the capacity of an Editor/Honorary Editor, or Associate Editor, and published 15 books as an editor. Carlo Cattani is a Professor of Mathematical Physics whose research spans applied mathematics, wavelet theory, nonlinear systems, multiscale analysis, and fractional calculus. His work focuses on the development of mathematical and computational methods for modeling complex phenomena in physics, engineering, biomedical systems, and image analysis. He has contributed to the advancement of multiscale and fractal-based approaches and their integration with modern data-driven methodologies. His research interests include mathematical modeling, signal and image processing, inverse problems, and interdisciplinary applications of applied mathematics. Professor Cattani has authored over 300 scholarly publications and several research monographs in applied mathematics and related fields. He is actively involved in international research collaborations that connect mathematical theory with practical challenges in science, engineering, and healthcare applications. Dr. Shaher Momani is Dean of the College of Humanities and Sciences at Ajman University, United Arab Emirates, and Distinguished Professor of Mathematics at the University of Jordan. He has previously been Dean of Scientific Research, Dean of Faculty of Science, and Head of Department of Mathematics at The University of Jordan. Dr. Momani has received numerous academic honors in the course of his career, including among many others The Order of King Abdullah II Ibn Al Hussein for Academic Contributions in Scientific Research, Jordanian Star of Science, ISI Web of Science Highly-Cited Interdisciplinary Researcher, ISI Web of Science Highly-Cited Researcher in Mathematics, named by Clarivate Analytics as one of the World’s Most Influential Scientific Minds 2014-2018, Liouville Award for Lifetime Achievement in Fractional Calculus, and the Mittag-Leffler Award for Fractional Differentiation and Its Applications. Dr. Momani has been classified as the top scientist in the world in terms of publications in fractional differential equations according to Clarivate and Scopus from 2008-2015, currently with 6959 Scopus citations. Dr. Momani is Editor in Chief of Numerical and Computational Methods in Sciences and Engineering. His research interests include Mathematical Modelling, Fractional Dynamical Systems, Numerical solution of ordinary and partial differential equations of fractional order, theory of fractional differential equations and integral equations, Newtonian and non-Newtonian fluid dynamics, stability of fractional linear systems, fractional order modelling and control in Biomedical Engineering, variational inequalities and obstacle problems, Mathematical Biology, and Mathematical Physics.

• 1. Introduction and Overview 2. Modelling Capillary Absorption in Building Materials with Emphasis on the Fourth Root Time Law 3. Fractional Velocities 4. Quintic and Quinticated Oscillators5. Krasnoselskii-Type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion 6. Computational Preconditioned Gauss-Seidel via Half-Sweep Approximation to Caputo's Time-Fractional Differential Equations7. Congruence between Mild and Classical Solutions of Generalized Fractional Impulsive Evolution Equation8. On the Conformable Fractional Triple Sumudu Transform and its Applications 9. Numerical Approximation of the General Model of Fractional Partial DifferentialEquations Arising in Science and Engineering10. Fractional Space of Sobolev Type with Riemann-Liouville Fractional Derivative11. Fractional Differential Equation Model for RLC Circuits12. Fractional Calculus-Based Dynamic Systems13. Soliton Solution of Damped KdV Equation in Unmagnetized SuperthermalPlasmas: Application of Adomian Decomposition Method14. (ω, ρ)-BVP for Impulsive Differential Equations of Fractional Order on Banach Space15. An Optimal Control Analysis of HIV/Visceral Leishmaniasis Co-Infection Model16. A General-Purpose Fractional Order Optimal Control Problem (FOOCP) Solver and a Benchmark on Optimal Vaccination Control of a Pandemic