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An eigenvalue problem in fractional h-discrete calculus

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Abstract

In this paper, we prove existence of solutions for an eigenvalue problem in the fractional h-discrete calculus. Dirichlet type boundary conditions are considered. Several properties for Green’s function of the associated problem are proven. A fixed point theorem in Cone theory is a main tool to obtain sufficient conditions on upper and lower bounds for eigenvalues of the boundary value problem so that the existence of positive solutions are guaranteed.

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Authors and Affiliations

  1. Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky, 42101-3576, USA

    F. M. Atıcı

  2. Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad, Telangana, 500078, India

    J. M. Jonnalagadda

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  1. F. M. Atıcı
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  2. J. M. Jonnalagadda
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Correspondence to F. M. Atıcı.

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Atıcı, F.M., Jonnalagadda, J.M. An eigenvalue problem in fractional h-discrete calculus. Fract Calc Appl Anal 25, 630–647 (2022). https://doi.org/10.1007/s13540-022-00028-0

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  • DOI: https://doi.org/10.1007/s13540-022-00028-0

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