h. h. g. hashem

Phenomena depending on their past history or their past state have received more importance. The mathematical models of these phenomena can be described by differential equations of a hereditary or a self-referred type. This paper is devoted to study the solvability of a state-dependent or self-referred integral equation via Chandrasekhar kernel. The investigation of this problem is motivated by the results from, Eder [10], Feˇckan [11] and Buica [3] who initiated the study of state dependent differential equations. Here, the existence and the uniqueness of the solution of this state-dependent integral equation via Chandrasekhar kernel have been discussed. The data dependency of the solution on some functions has been studied.

In this article, we discuss two boundary value problems for fractional-order differential equations. We show unique solutions exist and some data continuous dependence, with aim of proving some characteristics for these solutions of a coupled system of conjugate orders. These coupled systems are equivalent to coupled systems of second-order differential equations. Therefore, the analysis of the spectra of these problems is a consequence of that of second-order differential equations.