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On the Existence and Multiplicity of Solutions for Dirichlet’s problem for Fractional Differential equations

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Abstract

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Palermo, 90123, Palermo, Italy

    Diego Averna & Elisabetta Tornatore

  2. Department of Mathematics, University of Ruse, 7017, Ruse, Bulgaria

    Stepan Tersian

  3. Institute of Mathematics and Informatics Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Stepan Tersian

Authors
  1. Diego Averna
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  2. Stepan Tersian
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  3. Elisabetta Tornatore
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Correspondence to Diego Averna.

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Averna, D., Tersian, S. & Tornatore, E. On the Existence and Multiplicity of Solutions for Dirichlet’s problem for Fractional Differential equations. FCAA 19, 253–266 (2016). https://doi.org/10.1515/fca-2016-0014

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  • DOI: https://doi.org/10.1515/fca-2016-0014

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