Abstract
In this paper we study the existence of solution for the differential equation of arbitrary ( fractional) orders,with the general form of internal nonlocal condition,The problem with nonlocal integral condition will be studied.
Highlights
Problems with non-local conditions have been extensively studied by several authors in the last two decades
In this work we study the existence of at least one solution for the nonlocal problem of the arbitrary order differential equation dx t = f t, D x t, t 0,1 and 0,1 (1) dt with the general nonlocal condition ak x k = bj x j, (2)
We deduce the existence of solution for the nonlocal problem of the differential (1) with the integral condition
Summary
Problems with non-local conditions have been extensively studied by several authors in the last two decades. The reader is referred to ([1,2,3,4,5,6,7,8,9,10]), and references therein. K =1 j =1 where k a, c 0,1 , j d, b 0,1 , c d and 0 is parameter. We deduce the existence of solution for the nonlocal problem of the differential (1) with the integral condition c a x.
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