# Anti-periodic BVP for Volterra integro-differential equation of fractional order $1<\alpha \leq 2$, involving Mittag-Leffler function in the kernel

Volume 9, Issue 2, pp 452--460
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### Authors

Hüseyin Aktuğlu - Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey. Mehmet Ali Özarslan - Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey.

### Abstract

In this paper, we consider an anti-periodic Boundary Value Problem for Volterra integro-differential equation of fractional order $1<\alpha \leq 2$; with generalized Mittag-Leffler function in the kernel. Some existence and uniqueness results are obtained by using some well known fixed point theorems. We give some examples to exhibit our results.

### Share and Cite

##### ISRP Style

Hüseyin Aktuğlu, Mehmet Ali Özarslan, Anti-periodic BVP for Volterra integro-differential equation of fractional order $1<\alpha \leq 2$, involving Mittag-Leffler function in the kernel, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 2, 452--460

##### AMA Style

Aktuğlu Hüseyin, Özarslan Mehmet Ali, Anti-periodic BVP for Volterra integro-differential equation of fractional order $1<\alpha \leq 2$, involving Mittag-Leffler function in the kernel. J. Nonlinear Sci. Appl. (2016); 9(2):452--460

##### Chicago/Turabian Style

Aktuğlu, Hüseyin, Özarslan, Mehmet Ali. "Anti-periodic BVP for Volterra integro-differential equation of fractional order $1<\alpha \leq 2$, involving Mittag-Leffler function in the kernel." Journal of Nonlinear Sciences and Applications, 9, no. 2 (2016): 452--460

### Keywords

• Fractional derivative
• fractional integral
• Caputo fractional derivative
• boundary value problem
• Caputo fractional boundary value problem
• integral operators
• Mittag-Leffler functions.

•  34A08
•  34B15

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