Solutions of boundary value problems on extended-Branciari b-distance

Abstract

In this paper, we consider a new distance structure, extended Branciari b-distance, to combine and unify several distance notions and obtain fixed point results that cover several existing ones in the corresponding literature. As an application of our obtained result, we present a solution for a fourth-order differential equation boundary value problem.

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] .…”

New results concerning to approximate controllability of Hilfer fractional neutral stochastic delay integro‐differential systems

“…Many excellent monographs give the essential conceptual instruments to the subjective assessment of this investigation area. On the other hand, showing the interlinking similarly as the separation among classical and fractional differential representations, the readers can refer the monographs [1][2][3][4][5][6][7][8][9][10][11] and the research articles [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Neutral systems appear in numerous areas concerned with applied mathematics; consequently, neutral systems gained more consideration in the existing era.…”