Non-linear Set-Valued Delay Functional Integral Equations of Volterra-Stieltjes Type: Existence of Solutions, Continuous Dependence and Applications

In this chapter, we established two existence theorems for the non-linear Volterra-Stieltjes integral inclusion. The continuous dependence of the solutions on the delay functions, gi (i = 1,2) and on the set of selections, will be proved. The nonlinear Chandrasekhar set-valued functional integral equation and a non-linear Chandrasekhar quadratic functional integral equation, also the set-valued fractional orders integral equation, are studied as an application. An initial value problem of fractional-orders set-valued integro-differential equation will be considered.

Keywords: Non-linear functional integral equation, Volterra-Stieltjes integral inclusion, Chandrasekhar quadratic integral equation, Function of bounded variation, Continuous dependence, Differential inclusion, Delay function.