Search

In this article, two types of contractive conditions are introduced, namely extended integral Ϝ -contraction and (ϰ , Ω - Ϝ) -contraction. For the case of two mappings and their coincidence point theorems, a variant of (ϰ , Ω - Ϝ) -contraction has been introduced, which is called (ϰ , Γ 1 , 2 , Ω - Ϝ) -contraction. In the end, the applications of an extended integral Ϝ -contraction and (ϰ , Ω - Ϝ) -contraction are given by providing an existence result in the solution of a fractional order multi-point boundary value problem involving the Riemann–Liouville fractional derivative. An interesting existence result for the solution of the nonlinear Fredholm integral equation of the second kind using the (ϰ , Γ 1 , 2 , Ω - Ϝ) -contraction has been proven. Herein, an example is established that explains how the Picard–Jungck sequence converges to the solution of the nonlinear integral equation. Examples are given for almost all the main results and some graphs are plotted where required. [ABSTRACT FROM AUTHOR]

Fractional Differential inclusions, the multivalued version of fractional differential equations, yellow play a vital role in various fields of applied sciences. In the present article, a class of q-rung orthopair fuzzy (q-ROF) set valued mappings along with q-ROF upper/lower semi-continuity have been introduced. Based on these ideas, existence theorems for a numerical solution of a distinct class of fractional differential inclusions have been achieved with the help of Schaefer type and Banach contraction fixed point theorems. A physical example is also provided to validate the hypothesis of the main results. The notion of q-rung orthopair fuzzy mappings along with the use of fixed point techniques and a new-fangled Caputo type fractional derivative are the principal novelty of this article. [ABSTRACT FROM AUTHOR]