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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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