Extended existence results for FDEs with nonlocal conditions

Abstract

<abstract><p>This paper discusses the existence of solutions for fractional differential equations with nonlocal boundary conditions (NFDEs) under essential assumptions. The boundary conditions incorporate a point $ 0\leq c < d $ and fixed points at the end of the interval $ [0, d] $. For $ i = 0, 1 $, the boundary conditions are as follows: $ a_{i}, b_{i} > 0 $, $ a_{0} p(c) = -b_{0} p(d), \ a_{1} p^{'}(c) = -b_{1} p^{'}(d) $. Furthermore, the research aims to expand the usability and comprehension of these results to encompass not just NFDEs but also classical fractional differential equations (FDEs) by using the Krasnoselskii fixed-point theorem and the contraction principle to improve the completeness and usefulness of the results in a wider context of fractional differential equations. We offer examples to demonstrate the results we have achieved.</p></abstract>