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The main objective of this work is to use the Krein{Rutman theorem to characterize extremal points for a (n; p)-type Riemann{Liouville fractional-order boundary value problem. The key premise is that a mapping from a linear, compact operator to its spectral radius, which depends on =, is continuous and strictly increasing as a function of =. A nonlinear problem is also treated as an application of the result for the linear case's extremal point. [ABSTRACT FROM AUTHOR]

The main goal of this study is to seek optimal eigenvalue intervals of Χ1, Χ2,... Χn-1·Χn for which the iterative system of Riemann-Liouville type nonlinear p-Laplacian fractional boundary value problems has positive solutions under appropriate conditions. To demonstrate the positivity of solutions to these kinds of problems in a Banach space. we present an example as our conclusion. [ABSTRACT FROM AUTHOR]

In this paper, we consider an iterative system of Hadamard fractional boundary value problems. The sufficient conditions are derived for the existence of at least one positive solution by utilizing Guo-Krasnosel'skii fixed point theorem. The obtained results in the paper are illustrated with an example for their feasibility. [ABSTRACT FROM AUTHOR]

In this work we establish the existence of at least three positive solutions to a system of fractional order boundary value problems by an application of five functionals fixed point theorem. [ABSTRACT FROM AUTHOR]

This paper establishes the existence of a positive solution of fractional order two-point boundary value problem, Daq1 + y(t) + f(t, y(t)) = 0, t ∈[a, b], y(a) = 0, y'(a) = 0, α Daq2 + y(b) - β Daq3 + y(a) = 0, where Daqi +, i = 1, 2, 3 are the standard Riemann-Liouville fractional order derivatives, 2 < q1 ≤ 3, 0 < q2, q3 < q1, α, β are positive real numbers and b > a ≥ 0, by an application of lower and upper solution method and fixed-point theorems. [ABSTRACT FROM AUTHOR]

This paper establishes the existence of at least three positive solutions for a coupled system of p-Laplacian fractional order twopoint boundary value problems, ... by applying five functionals fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of at least three positive solutions for a coupled system of Riemann-Liouville fractional order two-point boundary value problems, by using an Avery generalization of the Leggett-Williams fixed point theorem. And then, we establish the existence of at least 2k - 1 positive solutions to the fractional order boundary value problems for an arbitrary positive integer k. [ABSTRACT FROM AUTHOR]