Local existence theorems for ordinary differential equations of fractional order

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 1982Publisher:Springer Berlin Heidelberg

Authors: Ahmad Zain; Alabedeen Mohammad Tazali;

doi: 10.1007/bfb0065037

Local existence theorems for ordinary differential equations of fractional order

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Abstract

In this paper, we prove two local existence theorems, by using both the Picard method and the Schauder fixed-point theorem, for the following initial-value problem: $$g(\alpha )(x) = f(x,g(x))(almost all x\varepsilon [a,a + h])$$ with (A) $$g(\alpha - 1)(a) = b\Gamma (\alpha ),0 0; b is a real number, and under suitable conditions on the function f.

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