Existence results for fractional impulsive integro-differential equations with integral conditions of Katugampola type. (English) Zbl 1481.45007
Summary: We study the existence and uniqueness of solutions of impulsive fractional integro-differential equations of order \(\alpha_1 \in (2, 3]\) with the Katugampola integral boundary conditions. Krasnoselkii’s fixed point theorem and Banach contraction principle are used to prove the existence and uniqueness results. An example is also presented at the end.
MSC:
| 45J05 | Integro-ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 34A37 | Ordinary differential equations with impulses |
| 47H10 | Fixed-point theorems |
Keywords:
fractional differential equations; Katugampola derivative; fractional derivative and integrals; existence and uniqueness; fixed point theoremsReferences:
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| [31] | P. Karthikeyan, Department of Mathematics, Sri Vasavi College, Erode, TN, 638316, India, e-mail: pkarthisvc@gmail.com |
| [32] | K. Venkatachalam, Department of Mathematics, Sri Vasavi College, Erode, TN, 638316, India, e-mail: arunsujith52@gmail.com |
| [33] | S. Abbas, School of Basic Science, Indian Institute of Technology Mandi, H.P., 175005, India, e-mail: abbas@iitmandi.ac.in |
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