2017
DOI: 10.15672/hjms.2017.463
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Abstract: A new and dierent approach to the investigation of the existence and uniqueness of solution of nonhomogenous impulsive boundary value problems involving the Caputo fractional derivative of order α (1 < α ≤ 2) is brought by using Lyapunov type inequality. To express and to analyze the unique solution, Green's function and its bounds are established, respectively. As far as we know, this approach based on the link between fractional boundary value problems and Lyapunov type inequality, has not been revealed even… Show more

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Cited by 3 publications
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“…The function y is a solution of the boundary value problem (60) if and only if y satisfies the integral equation…”
Section: Theorem 13 (A) If Problem (59) Has a Nontrivial Solution Thenmentioning
confidence: 99%
“…The function y is a solution of the boundary value problem (60) if and only if y satisfies the integral equation…”
Section: Theorem 13 (A) If Problem (59) Has a Nontrivial Solution Thenmentioning
confidence: 99%
“…Studying the qualitative properties of differential equations in the framework of fractional derivatives such as the existence and uniqueness, stability and controllability have pulled the attention of many researchers. Since the fixed point theories play an important role in the existence uniqueness issue, scientists have started to their contemporary result to fractional differential or integral equations see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][34][35][36][37][38][39].…”
Section: Introductionmentioning
confidence: 99%