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Continuous solutions of some fractional order integral equations

Salem H. A. H., El-Sayed A. M. A., Moustafa O. L.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2002

[Z] 42(2)

209-220

In this paper, Schauder fixed point theorem is used to prove an existence of positive continuous solutions for the nonlinear fractional order integral equation x(t) = h(t) + λ Iα (ƒ(x(t)) + g(x(t))), t ϵ [0, 1], α > 0 (E), where ƒ and g are nonlinear continuous functions and ƒ is nondecreasing while g is nonincreasing. Also the existence of maximal and minimal solutions of (E) will be proved. Some fractional order differential equations will be considered.