EXTREMAL POINTS FOR A (n; p)-TYPE RIEMANN{LIOUVILLE FRACTIONAL-ORDER BOUNDARY VALUE PROBLEMS

EXTREMAL POINTS FOR A (n, p)-TYPE RIEMANN{LIOUVILLE FRACTIONAL-ORDER BOUNDARY VALUE PROBLEMS

B. M. B. KRUSHNA

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Abstract. 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 bound- ary value problem. The key premise is that a mapping from a linear, compact operator to its spectral radius, which depends on ℑ, is continuous and strictly increasing as a function of ℑ. A nonlinear problem is also treated as an application of the result for the linear case's extremal point.

Keywords: Fractional derivative, Boundary value problem, Extremal point.

AMS Subject Classification:26A33, 34B08, 47A30.