Title of the talk: "Numerical Approximation Scheme for Distributed Order Fractional Differential Equations. "

Date , Time & Venue: 18 August 2025  at 12 PM on Seminar Hall, Dept. of Mathematics

Abstract:  In this work, we propose a novel method for approximating solutions to distributed-order fractional differential equations in both single-variable and twovariable cases, using Legendre wavelets. Our approach combines the LegendreGauss quadrature formula with the Tau method to construct an operational matrix specifically for distributed-order Legendre wavelets. This matrix enables the efficient conversion of the original fractional differential equations into systems of linear algebraic equations. To demonstrate the accuracy and effectiveness of the proposed method, we present several illustrative test problems.

About the Speaker: Dr. Yashveer Kumar earned his Ph.D. in Mathematics from the Indian Institute of Technology (BHU) Varanasi, India, in 2023. Following his doctoral studies, he served as an Assistant Professor in the Department of Mathematics at Siksha ‘O’ Anusandhan (SOA) University, Bhubaneswar, from September 2023 to August 2024. In August 2024, Dr. Kumar joined one of the Portuguese research centre INESC-ID, Lisboa, Lisbon, Portugal, as a postdoctoral researcher, where he is currently engaged in advanced research on numerical solutions of fractional differential equations, with a particular focus on Monte Carlo simulation techniques. He has published six research articles in peer-reviewed journals, and three more are currently under review. His research interests lie at the intersection of fractional calculus, numerical analysis, stochastic methods, and operational matrix method.