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Existence of Solutions for Nonlinear Integro-Differential Equations via Fixed Point Theory

 

 

1. D. Bhosale¹ and R. B. Deshmukh²

¹Research Scholar, Mathematics Research Centre, Dayanand Science College, Latur, Maharashtra, India

²Asst.Prof., Department of Computer Science, Rajarshi Shahu mahavidyalay Latur, Maharashtra, India

Email: pavanrajed80@gmail.com , drutuja912@gmail.com

 

Abstract: Fixed point theory has emerged as a powerful analytical tool in the study of nonlinear differential and integro-differential equations. This work explores the existence of solutions for a class of first-order nonlinear problems involving both differential and integral operators, which naturally appear in models describing memory-dependent or hereditary processes. By transforming the original problem into an equivalent operator equation in a Banach space and applying classical fixed point results such as the Banach Contraction Principle and the Schauder Fixed Point Theorem, we establish general conditions that ensure the existence of solutions. Under stronger assumptions, uniqueness is also discussed. The methodology extends traditional techniques for ordinary differential equations and provides a unified framework suitable for problems with nonlocal behavior.

Keywords: Fixed Point Theory, Integro-Differential Equations, Nonlinear Analysis, Banach Space, Existence of Solutions, Schauder Theorem.

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