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Zbl 1240.26009
Hussein, A.H.Salem
Fractional order boundary value problem with integral boundary conditions involving Pettis integral. (English)
[J] Acta Math. Sci., Ser. B, Engl. Ed. 31, No. 2, 661-672 (2011). ISSN 0252-9602

Summary: We investigate the existence of pseudo-solutions to a fractional order boundary value problem with integral boundary conditions in the Banach space of continuous functions equipped with the weak topology. The class of problems of this type is very interesting and important. It includes two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be a Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
34G20 Nonlinear ODE in abstract spaces

Keywords: fractional calculus; pseudo solution; boundary value problem; Pettis integrals

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