Novel Approaches to Positive Solutions for Fractional Nonlinear Boundary Value Problems

Abstract

This study explores a fractional boundary value problem based on Riemann-Liouville derivatives and integrals. New results are derived to begin the necessary and adequate circumstances for the existence and uniqueness of positive solutions, leveraging fixed-point theorems on right circular cones. A convergent iterative sequence for solving the problem is presented, along with a numerical scheme. The validity of the results is demonstrated through illustrative examples.