Existence and multiplicity for some boundary value problems involving Caputo and Atangana–Baleanu fractional derivatives: A variational approach

Amjad Salari and Behzad Ghanbari

Chaos, Solitons & Fractals, 2019, vol. 127, issue C, 312-317

Abstract: In this paper, we study the existence and the numerical estimates of solutions for a specific types of fractional differential equations. The nonlinear part of the problem, however, presupposes certain hypotheses. Particularly, for exact localization of the parameter, the existence of a non-zero solution is established, which requires the sublinearity of the nonlinear part at the origin and infinity. We also take into consideration several theoretical and numerical examples. One of the main novelties of this paper is to use the variational method to investigate the properties of solutions of boundary values problems involving Atangana–Baleanu fractional derivative for the first time.

Keywords: Fractional differential equations; Multiple solutions; Variational methods; Critical point theory; Numerical solution; Atangana–Baleanu fractional derivative (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:127:y:2019:i:c:p:312-317

DOI: 10.1016/j.chaos.2019.07.022

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