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

Agarwal, Ravi P ; Lupulescu, Vasile ; O’Regan, Donal ; ur Rahman, Ghaus

Agarwal, Ravi P

Lupulescu, Vasile

O’Regan, Donal

ur Rahman, Ghaus

##### Repository DOI

##### Publication Date

2013-01-01

##### Type

Article

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##### Citation

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 ,

##### 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.

##### Funder

##### Publisher

Springer Nature

##### Publisher DOI

10.1186/1687-1847-2013-302

##### Rights

Attribution-NonCommercial-NoDerivs 3.0 Ireland