Discontinuity, Nonlinearity, and Complexity
Existence of Solutions for Boundary Value Problem of Nonlinear Integrodifferential Equations of Fractional Order
Discontinuity, Nonlinearity, and Complexity 8(1) (2019) 5770  DOI:10.5890/DNC.2019.03.006
J. Kavitha$^{1}$, V. Sadhasivam$^{2}$
$^{1}$ Department of Mathematics, Sona College of Technology (Autonomous), Salem Dt, Salem636005, 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 integrodifferential 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 integrodifferential 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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