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

Boundary Value Problems for Impulsive Fractional Evolution Integrodifferential Equations with Gronwall’s Inequality in Banach Spaces

Discontinuity, Nonlinearity, and Complexity 3(1) (2014) 33--48 | DOI:10.5890/DNC.2014.03.003

Dimplekumar N. Chalishajar$^{1}$; K. Karthikeyan$^{2}$

1Department of Applied Mathematics, Virginia Military Institute (VMI), 431 Mallory Hall, Lexington, VA-24450, USA

$^{2}$ Department of Mathematics, KSR College of Technology, Tiruchengode-637 215, Tamilnadu, India

Abstract

In this paper, we study boundary value problems for impulsive fractional evolution integrodifferential equations with Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions. An example is given to illustrate the results.

Acknowledgments

1. First author expresses his thanks to Jackson-Hope grant of VMI (J-H 2014) for kind support.. 2. Authors express their gratitude to the anonymous referee for valuable comments and suggestions which are helpful to modify the manuscript.

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