A New Approach to the Solution of Non-Linear Integral Equations via Various FBe-Contractions

Abstract

In this article, we introduce and establish various approaches related to the F-contraction using new sorts of contractions, namely the extended F B e -contraction, the extended F B e -expanding contraction, and the extended generalized F B e -contraction. Thereafter, we propose a simple and efficient solution for non-linear integral equations using the fixed point technique in the setting of a B e -metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples where necessary.

On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions

“…On the other hand, the fixed point theory is a collection of results saying that a mapping T will have at least one fixed point (i.e., T(x) = x), under some conditions on T. Results of this kind are of paramount importance in many areas of mathematics, other sciences, and engineering. So, some recent articles which are pertinent to the fixed point theory can found in [22][23][24][25][26][27][28][29]. The existence and uniqueness of solutions for different classes of fractional differential equations (FDEs) with initial or boundary conditions have been studied by several researchers; see [30][31][32][33][34][35][36][37][38] and the references therein.…”

Solutions of the Nonlinear Integral Equation and Fractional Differential Equation Using the Technique of a Fixed Point with a Numerical Experiment in Extended b-Metric Space

“…For more interesting examples and basic results in δ e -metric space, we refer to [16][17][18][19][20]. For some recent modifications or developments to extended b−metric spaces, the reader may refer to the so-called controlled and double-controlled metric type spaces in [21,22] and for further fixed point investigations in extended b-metric spaces to [23].…”

Generalized Contractions on Extended \(b\)-Metric Space Endowed With a Graph

“…Kamran et al [21] proposed the notion of extended b-metric space in 2017. For more information in this space (see [3,7,18,19,[23][24][25]). Errai et al [16] recently acquired various Ćirić-Rus-Reich type and interpolative Hardy-Rogers type contraction mapping results.…”