Analytical and Numerical Analysis of A Generalized Non Standard Volterra Integro-Differential Equations

Abstract

• Fredholm and Volterra integral equations hold a significant position in mathe- matics due to their wide-ranging applications across various scientific fields.

• In this thesis, we focus on a specific form of the non linear, non standard, integro-differential Volterra equation.

• Using Schauder fixed point theorem, we establish the existence and unique- ness for the solution of this integro-differential Volterra equation under well-defined

conditions. • We then apply the Fibonacci Wavelet Collocation method to obtain an approximate solution to this integro-differential equation, followed by illustrative examples demonstrating the obtained results.