Fixed Point Results and its Applications to the Systems of Non-linear Integral and Differential Equations of Arbitrary Order

Abstract

In this manuscript, common fixed point results for self-mappings satisfying generalized weak integral type contraction in the setting of G-metric space are established. Using the derived results, some applications to the systems of non-linear integral and fractional differential equations are also discussed.

On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions

“…. Besides from the aforesaid problems, recently by using fixed point theory, several remarkable problems have been investigated in FDEs with various boundary conditions, for detail see [2,7,28] and the references therein. Sometimes in many applications like numerical analysis, optimization, mathematical biology, business mathematics, economics etc., we come across the situation where finding the exact solution is quite difficult task.…”

Analytical Solution for Differential and Nonlinear Integral Equations via F ϖ

“…There are developments to translate fixed point theorems into nonlinear integral equations and differential equations (for related works and developments, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20]).…”

Some fixed point results of F-Contraction mapping in D-metric spaces by Samet’s method

“…Also, they have studied properties of S-metric spaces and some fixed point results for a self-map on an S-metric space. In the following, some authors extended this work (see [2,20,24,25]). Samet et al [23,22] proved that α − φ contractions unify large classes of contractive type operators, whose fixed points can be obtained by means of the Picard iteration.…”