Approximation of functions in Holder class by third kind Chebyshev wavelet and its application in solution of Fredholm integro-differential equations

This paper presents numerical solutions to Fredholm integro-differential equations that arise in physical, chemical, engineering, and biological models using approximations by third kind Chebyshev wavelet. A third kind Chebyshev wavelet is used to create an operational matrix, and a method for converting the problem into a system of algebraic equations is proposed. The convergence and error analysis of solution functions in Holder class using moduli of continuity are also developed. Illustrative examples are provided to demonstrate the effectiveness of the proposed method, and the method is extended to find a solution to a suspension bridge model encountered in engineering.