Browsing by Author "Erhan,I.M."

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Citation - Scopus: 5
Adomian Polynomials Method for Dynamic Equations on Time Scales
(DergiPark, 2021) Georgiev,S.G.; Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
A recent study on solving nonlinear differential equations by a Laplace transform method combined with the Adomian polynomial representation, is extended to the more general class of dynamic equations on arbitrary time scales. The derivation of the method on time scales is presented and applied to particular examples of initial value problems associated with nonlinear dynamic equations of first order. © 2021, DergiPark. All rights reserved.
Citation - Scopus: 11
Different Types Meir-Keeler Contractions on Partial Metric Spaces
(2012) Erhan,I.M.; Karapinar,E.; Türkoǧlu,D.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this manuscript, Meir-Keeler contractions on partial metric spaces are introduced. It is shown that if a self-mapping T on a complete partial metric spaces is a Meir-Keeler contraction, then T has a unique fixed point. © 2012 EUDOXUS PRESS, LLC.
Divided and A-Divided Differences on Time Scales
(De Gruyter, 2023) Jaddoa,N.; Sevinik-Adigüzel,R.; Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this chapter, the divided differences and cr-divided differences on time scales are introduced. The Newton and cr-Newton interpolation polynomial are constructed. In addition, the Hermite interpolation polynomial on time scales is constructed by using the divided differences table. Examples are presented to illustrate the theoretical results. © 2023 Walter de Gruyter GmbH, Berlin/Bostonl. All rights reserved.
Citation - Scopus: 74
Fixed Points of Generalized Α-Admissible Contractions on B-Metric Spaces With an Application To Boundary Value Problems
(Yokohama Publications, 2016) Aksoy,Ü.; Karapinar,E.; Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
A general class of α-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations. © 2016.
Citation - Scopus: 1
Fixed Points of Α -Admissible Mappings on Partial Metric Spaces
(Hindawi Publishing Corporation, 2014) Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, a general class of α-admissible contractions on partial metric spaces is introduced. Fixed point theorems for these contractions on partial metric spaces and their consequences are stated and proved. Illustrative example is presented. © 2014 Inci M. Erhan.
Citation - Scopus: 1
Numerical Analysis on Time Scales
(De Gruyter, 2022) Georgiev,S.G.; Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Mathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques. This textbook discusses the design, analysis and applications of computational techniques for dynamic equations on time scales. Hands-on examples utilizing MATLAB are provided as well as end of chapter problems. © 2022 Walter de Gruyter GmbH, Berlin/Boston. All rights reserved.
On a Generalized Α-Admissible Rational Type Contractive Mapping
(Yokohama Publications, 2016) Erhan,I.M.; Kir,M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Recently, many generalized contractive conditions which involve rational contractive inequalities have been introduced in the context of partially ordered metric spaces. In this paper, we aim to give a generalized rational contractive condition which involves some of these results without need of extra restrictions. © 2016.
Citation - Scopus: 5
SERIES SOLUTION METHOD FOR CAUCHY PROBLEMS WITH FRACTIONAL Δ-DERIVATIVE ON TIME SCALES
(Element D.O.O., 2019) Georgiev,S.G.; Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper we introduce a series solution method for Cauchy problems associated with Caputo fractional delta derivatives on time scales with delta differentiable graininess function. We also apply the method to Cauchy problems associated with dynamic equations and present some illustrative examples. © The Author(s) 2019.