Extensions of almost- F and F-Suzuki contractions with graph and some applications to fractional calculus.

In this paper, we introduce the two new concepts of an α-type almost- F-contraction and an α-type F Suzuki contraction and prove some fixed point theorems for such mappings in a complete metric space. Some examples and an application to a nonlinear fractional differential equation are given to illustrate the usability of the new theory. [ABSTRACT FROM AUTHOR]