Existence, Uniqueness, Boundedness and Continuous Dependence of Solutions for Fractional Order Fredholm Difference Equations
B. U. Lavhare
Department of Mathematics, Comrade GSP ASC College, Talasari, Palghar, Maharashtra, India.
H. L. Tidke *
Department of Mathematics, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, Maharashtra, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we investigate the existence and uniqueness of solutions to certain fractional-order Fredholmtype difference equation involving an iterated sum. In addition, we examine the boundedness and continuous dependence of solutions under various assumptions imposed on the associated functions. The results are established using finite difference inequalities with explicit estimates, and offer fundamental insights that may serve as a valuable reference for future research.
Keywords: Difference equation, fractional order, initial value problem, inequality