Opuscula Math. 36, no. 2 (2016), 215-238
http://dx.doi.org/10.7494/OpMath.2016.36.2.215

Opuscula Mathematica

# Solutions of fractional nabla difference equations - existence and uniqueness

Abstract. In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.

Keywords: nabla difference, exponential function, fixed point, existence, uniqueness, continuous dependence.

Mathematics Subject Classification: 34A08, 39A10, 39A99.

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• Department of Mathematics, Birla Institute of Technology and Science, Pilani Hyderabad Campus, Hyderabad - 500078, Telangana, India
• Communicated by Josef Diblík.
• Revised: 2015-09-14.
• Accepted: 2015-09-22.
• Published online: 2015-12-18.