Gronwall–Bellman Type Inequalities | Asian Journal of Pure and Applied Mathematics

An integro-differential equation is a mathematical equation that deals with the integrals and derivatives of an unknown function. In the study of differential, integral, and partial differential equations, integral inequality plays a significant role, and Gronwall inequality has benefited much from it.

In addition to our previous work, we give a new generalised Gronwall inequality by establishing the importance of our conclusions using two crucial lemmas. We next applied the inequality to a nonlinear integro-differential equation, demonstrating that the Gronwall-Bellman inequality is crucial in differential equations.

Please see the link :- https://globalpresshub.com/index.php/AJPAM/article/view/1337