New numerical scheme for solving integral equations via fixed point method using distinct (ω-F)-contractions

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.…”

Applying fixed point methods and fractional operators in the modelling of novel coronavirus 2019-nCoV/SARS-CoV-2

“…Any traditional discussions indicate that literature on this topic may infer that the concept of F -contraction is a typical generalization of the Banach contraction principle as a consequence of the uniqueness. For a extensive study on fixed points, F -contraction and fractionals the reader may refer [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] .…”

Orthogonal m-metric spaces and an application to solve integral equations

“…And in this context, we have improved and generalized some well-known results in the literature and developed some fixed point theorems for the proposed contraction. Inspired by the work of many scientist [14][15][16][17][18] regarding fixed point theorems to prove the existence and uniqueness of solutions for certain types of integral equations related to fractional type differential equations, we have also developed an illustrative example and a possible application for the system of Fredholm integral equations to claim the validity of the proposed results.…”