In this paper we study the existence of a unique solution of a nonlinear integral equation in the space of bounded variation on an unbounded interval by using measure of noncompactness and Darbo fixed point theorem.
In this article, we will investigate the existence and uniqueness of a bounded variation solution for a fractional integral equation in the space L1[0, T] of Lebesgue integrable functions.
In this paper, we consider a mixed integral equation (MIE) of the second kind. Under certain conditions, the existence of a unique solution of is discussed and proved. The kernel of position takes asingular form, while the kernel of time is continuous. Using a quadratic numerical method, the MIE leads us to a linear system of Fredholm integral equations (SFIEs). Then,SFIEsafter using Toeplitz matrix method (TMM),tends to a linear algebraic system (LAS). The existence of a unique solution of LAS is proved. Finally, numerical examples are considered, and the error, in each case, is calculated.
In this article, we will investigate the existence of a unique bounded variation solution for a functional integral equation of Volterra type in the space L1(R+) of Lebesgue integrable functions.
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