Some Novel Results on the Existence and Uniqueness of a Positive Solution to a Kind of Nonlinear Fractional Boundary Value Problems
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Authors: A. AHMADKHANLU, V. S. ERTURK AND P. KUMAR
DOI: 10.46793/KgJMat2604.613A
Abstract:
This work investigates a fractional boundary value problem in the sense of Riemann-Liouville derivative and integral. We derive some novel results for the necessary and sufficient conditions for the existence and uniqueness of the positive solution. In this regard, some fixed-point theorems on cones are used. Also, a convergent successive sequence to find the solution to the problem is introduced. We derive the numerical scheme for the proposed problems. The correctness of the proposed results is verified with some illustrative examples.
Keywords:
Fractional boundary value problem, Riemann-Liouville derivative and integral, Green’s function, fixed point theorem.
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