Electron. J. Differential Equations, Vol. 2017 (2017), No. 100, pp. 1-18.

Fractional boundary value problems with multiple orders of fractional derivatives and integrals

Sotiris K. Ntouyas, Jessada Tariboon

In this article we study a new class of boundary value problems for fractional differential equations and inclusions with multiple orders of fractional derivatives and integrals, in both fractional differential equation and boundary conditions. The Sadovski's fixed point theorem is applied in the single-valued case while, in multi-valued case, the nonlinear alternative for contractive maps is used. Some illustrative examples are also included.

Submitted February 21, 2017. Published April 11, 2017.
Math Subject Classifications: 34A08, 34A12, 34A60.
Key Words: Fractional differential equation; fractional differential inclusion; boundary value problem; existence; fixed point theorems.

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Sotiris K. Ntouyas
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece.
email: sntouyas@uoi.gr
Jessada Tariboon
Nonlinear Dynamic Analysis Research Center
Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok 10800, Thailand
email: jessada.t@sci.kmutnb.ac.th

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