Abstract
The existence of a parametric fractional integral equation and its numerical solution is a big challenge in the field of applied mathematics. For this purpose, we generalize a special type of fixed-point theorems. The intention of this work is to prove fixed-point theorems for the class of β−G, ψ−G contractible operators of Darbo type and demonstrate the usability of obtaining results for solvability of fractional integral equations satisfying some local conditions in Banach space. In this process, some recent results have been generalized. As an application, we establish a set of conditions for the existence of a class of fractional integrals taking the parametric Riemann–Liouville formula. Moreover, we introduce numerical solutions of the class by using the set of fixed points.
Highlights
A measure of noncompactness is a function demarcated on the class of all nonempty and bounded subsets of a definite metric space where it is identical to zero on the entire class of comparatively compact sets [1]
The authors introduced some applications of the measure of noncompactness notion to functional equations involving nonlinear integral equations of arbitrary orders, implicit arbitrary integral equations and q-integral equations of arbitrary orders
As an application, we demonstrate the applicability of our main result in establishing the existence of solutions of an integral equation of fractional order of the form: z(t) = u(t) +
Summary
A measure of noncompactness is a function demarcated on the class of all nonempty and bounded subsets of a definite metric space where it is identical to zero on the entire class of comparatively compact sets [1]. A survey of theory and applications of measures of noncompactness is presented in [2]. The normal measures of noncompactness are deliberated, and their possessions are associated. Some consequences regarding normal measures of noncompactness in altered spaces are offered. The authors introduced some applications of the measure of noncompactness notion to functional equations involving nonlinear integral equations of arbitrary orders, implicit arbitrary integral equations and q-integral equations of arbitrary orders. The measure of noncompactness plays very significant role in the theory of fixed points and applications
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