DOI: 10.24193/fpt-ro.2020.2.30

Authors: P. Borisut, P. Kumam, I. Ahmed and K. Sitthithakerngkiet

Abstract: In this paper, we study and consider the positive solution of fractional differential equation with nonlocal multi-point conditions of the from:


where n-1 < q < n, n ≥ 2, n-1 < p_i < n, q > p_i m, n ∈ ℕ, k=0,1,...,n-2, 0 < η₁ < η₂ < ... < κ, β_i ≤ 0, κ ∈ (0,1], are the Riemann-Liouville fractional derivative of order q, p_i, f:[0,1] × C([0,1],E) → E, E be Banach space and g:(0,1)→ℝ⁺ are continuous functions. The main tools for finding positive solutions of the above problem are the fixed point theorems of Guo-Krasnoselskii and of Boyd and Wong. An example is included to illustrate the applicability of our results.

Key Words and Phrases: Boundary value problems, Riemann-Liouville fractional derivative, fixed point theorems.

2010 Mathematics Subject Classification: 74H10, 54H25, 47H10.

Published on-line: July 1st, 2020.

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