## Multi-term fractional differential equations in a nonreflexive banach space

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2013-01-01##### Author

Agarwal, Ravi P

Lupulescu, Vasile

O’Regan, Donal

ur Rahman, Ghaus

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Agarwal, Ravi P; Lupulescu, Vasile; O’Regan, Donal; ur Rahman, Ghaus (2013). Multi-term fractional differential equations in a nonreflexive banach space. Advances in Difference Equations ,

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##### Abstract

In this paper we establish an existence result for the multi- term fractional differential equation
(D-alpha m - (m-1)Sigma(aiD alpha i)(i=1))u(t) = f(t, u(t)) for t epsilon [0, 1], u(0) = 0, (1)
where D(p)(alpha m)y(.) and D(p)(alpha i)y(.) are fractional pseudo- derivatives of a weakly absolutely continuous and pseudo- differentiable function u(.) : T -&gt; E of order alpha(m) and alpha(i), i = 1, 2,..., m - 1, respectively, the function f(t, .) : T x E -&gt; E is weakly-weakly sequentially continuous for every t is an element of T and f (., y(.)) is Pettis integrable for every weakly absolutely continuous function y(.) : T -&gt; E, T is a bounded interval of real numbers and E is a nonreflexive Banach space, 0 &lt; alpha(1) &lt; alpha(2) &lt; ... &lt;alpha(m) &lt; 1 and a(1), a(2),..., a(m-1) are real numbers such that a := Sigma(m-1)(i=1) vertical bar a(j)vertical bar/Gamma(alpha(m)-alpha(j)+1) &lt; 1.