ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Existence of Solutions for Boundary Value Problem of Non-linear Integro-differential Equations of Fractional Order

Discontinuity, Nonlinearity, and Complexity 8(1) (2019) 57--70 | DOI:10.5890/DNC.2019.03.006

J. Kavitha$^{1}$, V. Sadhasivam$^{2}$

$^{1}$ Department of Mathematics, Sona College of Technology (Autonomous), Salem Dt, Salem-636005, Tamil Nadu, India

$^{2}$ Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affili. Periyar University), Namakkal Dt, Rasipuram - 637401, Tamil Nadu, India

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Abstract

In this article, we cultivate the existence theory for the following boundary value problem of fractional integro-differential equations Dα u(t) = f(t,u(t), (φu)(t)), t ∈ [0,T], 1 <α ≤ 2, (φ u)(t)) = γ(t, s)u(s)ds, together with fractional integro-differential boundary conditions Dα−2u(0+) = 0, Dα−1u(0+) =νIα−1u(η), 0 <η < T. By using the coincidence degree theory, we will obtain a new criteria for the existence of the solutions of the given boundary value problems. We present an example to illustrate our main results.

Acknowledgments

The authors thank Prof.N. Kosmatov for his support to complete the paper and the referees for giving kind encouragement and suggestions for the improvement of this paper.

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