Existence and uniqueness results for boundary value problems of higher order fractional integro-differential equations involving gronwall's inequality in banach spaces |
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Authors: | Dimplekumar N. CHALISHAJAR K. KARTHIKEYAN |
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Affiliation: | 1. Department of Mathematics and Computer Science, Virginia Military Institute (VMI) 417 Mallory Hall, Lexington, VA 24450, USA;2. Department of Mathematics, KSR College of Technology, Tiruchengode-637 215, Tamilnadu, India |
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Abstract: | We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α ∈ (n-1,n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder's inequality, a suitable singular Gronwall's inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results. |
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Keywords: | Boundary value problems fractional order integro-differential equations boundary value problems existence and uniqueness singular gronwall inequality fixed point theorem |
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