Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives

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Basak Karpuz, Umut M. Ozkan, Tugba Yalcin, Mustafa K. Yildiz, Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives, Int. J. Anal. Appl., 13 (2) (2017), 216-230.

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Basak Karpuz, Umut M. Ozkan, Tugba Yalcin, Mustafa K. Yildiz

Abstract

In this paper, we extend the definition of the fractional integral and derivative introduced in [Appl. Math. Comput. 218 (2011)] by Katugampola, which exhibits nice properties only for numbers whose real parts lie in [0,1]. We prove some interesting properties of the fractional integrals and derivatives. Based on these properties, the following concepts for the new type fractional differential equations are explored: Existence and uniqueness of solutions; Solutions of autonomous fractional differential equations; Dependence on the initial conditions; Green's function; Variation of parameters formula.

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References

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