On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions

Volume 10, Issue 9, pp 4760--4775
Publication Date: September 12, 2017 Submission Date: March 14, 2017
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Authors

Arshad Ali - Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan. Faranak Rabiei - Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. - Institute For Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. Kamal Shah - Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan.

Abstract

In this manuscript, using Schaefer's fixed point theorem, we derive some sufficient conditions for the existence of solutions to a class of fractional differential equations (FDEs). The proposed class is devoted to the impulsive FDEs with nonlinear integral boundary condition. Further, using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss various kinds of Ulam-Hyers stability. Finally to illustrate the established results, we provide an example.

Share and Cite

ISRP Style

Arshad Ali, Faranak Rabiei, Kamal Shah, On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4760--4775

AMA Style

Ali Arshad, Rabiei Faranak, Shah Kamal, On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions. J. Nonlinear Sci. Appl. (2017); 10(9):4760--4775

Chicago/Turabian Style

Ali, Arshad, Rabiei, Faranak, Shah, Kamal. "On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4760--4775

Keywords

• Caputo fractional derivative
• integral boundary conditions
• impulsive condition
• fixed point theorem
• Ulam stability.

•  34A08
•  35R11
•  26A33

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