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Analyzing the existence of solution of a fractional order integral equation: A fixed point approach

Saha Dipankar, Sen Mausumi, Roy Santanu

Journal of Applied Analysis

2022

Vol. 28, nr 2

199--210

This paper signifies the beauty of fixed point theory in the context of attaining the sufficient condition for the existence of the solution of a non-linear functional-integral equation in an unbounded interval. Here a non-linear integral equation (NLIE) involving a fractional operator is taken in the form of an operator equation. Utilizing the perception of measure of noncompactness (MNC) along with certain relevant assumptions, it is proved that the operator equation satisfies the Darbo condition for the product of operators in a Banach algebra. Finally, the result obtained is verified by the assistance of the numerical example.