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Citation - WoS: 3
A New Transform Method in Nabla Discrete Fractional Calculus
(Springer, 2012) Jarad, Fahd; Kaymakcalan, Billur; Tas, Kenan
Starting from the definition of the Sumudu transform on a general nabla time scale, we define the generalized nabla discrete Sumudu transform. We obtain the nabla discrete Sumudu transform of Taylor monomials, fractional sums, and differences. We apply this transform to solve some fractional difference equations with initial value problems. MSC: 44A15, 44A55.
Citation - WoS: 14
Citation - Scopus: 24
Generalized Alpha-Psi Type Mappings of Integral Type and Related Fixed Point Theorems
(Springer, 2014) Tas, Kenan; Karapinar, Erdal; Shahi, Priya
The aim of this paper is to introduce two classes of generalized alpha-psi-contractive type mappings of integral type and to analyze the existence of fixed points for these mappings in complete metric spaces. Our results are improved versions of a multitude of relevant fixed point theorems of the existing literature.
Citation - WoS: 6
Citation - Scopus: 14
Generalized Diamond-Α Dynamic Opial Inequalities
(Springer, 2012) Lesaja, Goran; Tas, Kenan; Atasever, Nuriye; Kaymakcalan, Billur
We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this type. Also, we introduce an example to illustrate our result.

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