A novel approach to nonlinear fractional volterra integral equations

Abstract

Nonlinear Fractional Volterra integral equations (FVIEs) of the first kind present challenges due to their intricate nature, combining fractional calculus and integral equations. In this research paper, we introduce a novel method for solving such equations using Leibniz integral rules. Our study focuses on a thorough analysis and application of the proposed algorithm to solve fractional Volterra integral equations. By using Leibniz integral rules, we offer a fresh perspective on handling these equations, shedding light on their fundamental properties and behaviours. As a result of this study, we anticipate contributing distinctively to the broader development of analytical tools and techniques. By bridging the gap between fractional calculus and integral equations, our approach not only offers a valuable computational methodology but also paves the way for new insights into the application domains in which such equations arise.

Keywords

• integral equations
• fractional calculus
• Leibniz integral rule
• Mitteg-Leffler function
• Caputo fractional operator
• Riemann-Liouville fractional operator