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Öğe An Alternative Approach to the Axiomatic Characterization of the Interval Shapley Value(2024) Ekici, MustafaThis study presents a new approach to the axiomatic characterization of the interval Shapley value. This approach aims to improve our comprehension of the particular characteristics of the interval Shapley value in a provided context. Furthermore, the research contributes to the related literature by expanding and applying the fundamental axiomatic principles used to define the interval Shapley value. The proposed axioms encompass symmetry, gain-loss, and differential marginality, offering a distinctive framework for understanding and characterizing the interval Shapley value. Through these axioms, the paper examines and interprets the intrinsic properties of the value objectively, presenting a new perspective on the interval Shapley value. The characterization highlights the importance and distinctiveness of the interval Shapley value.Öğe APPLICATION OF THE RATIONAL (G?/G)-EXPANSION METHOD FOR SOLVING SOME COUPLED AND COMBINED WAVE EQUATIONS(Ankara Univ, Fac Sci, 2022) Ekici, Mustafa; Unal, MetinIn this paper, we explore the travelling wave solutions for some nonlinear partial differential equations by using the recently established rational (G'/G)-expansion method. We apply this method to the combined KdV-mKdV equation, the reaction-diffusion equation and the coupled Hirota-Satsuma KdV equations. The travelling wave solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values, the solitary waves are also derived from the travelling waves. We have also given some figures for the solutions.Öğe Exact Solutions of Time-Fractional Thin-Film Ferroelectric Material Equation with Conformable Fractional Derivative(2025) Ekici, MustafaThis study employs the unified method, a powerful approach, to address the intricate challenges posed by fractional differential equations in mathematical physics. The principal objective of this study is to derive novel exact solutions for the time-fractional thin-film ferroelectric material equation. Fractional derivatives in this study are defined using the conformable fractional derivative, ensuring a robust mathematical foundation. Through the unified method, we derive solitary wave solutions for the governing equation, which models wave dynamics in these materials and holds significance in various fields of physics and hydrodynamics. The behavior of these solutions is analyzed using the conformable derivative, shedding light on their dynamic properties. Analytical solutions, formulated in hyperbolic, periodic, and trigonometric forms, illustrating the impact of fractional derivatives on these physical phenomena. This paper highlights the capability of the unified method in tackling complex issues associated with fractional differential equations, expanding both mathematical techniques and our understanding of nonlinear physical phenomena.Öğe Exact Solutions to Some Nonlinear Time-Fractional Evolution Equations Using the Generalized Kudryashov Method in Mathematical Physics(Mdpi, 2023) Ekici, MustafaIn this study, we utilize the potent generalized Kudryashov method to address the intricate obstacles presented by fractional differential equations in the field of mathematical physics. Specifically, our focus centers on obtaining novel exact solutions for three pivotal equations: the time-fractional seventh-order Sawada-Kotera-Ito equation, the time-fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation, and the time-fractional seventh-order Kaup-Kupershmidt equation. The generalized Kudryashov method, celebrated for its versatility and efficacy in addressing intricate nonlinear problems, plays a central role in our research. This method not only simplifies the equations but also unveils their inner dynamics, rendering them amenable to meticulous analysis. It is worth noting that our fractional derivatives are defined in the context of the conformable fractional derivative, providing a solid foundation for our mathematical investigations. One notable aspect of our study is the visual representation of our findings. Graphical representations of the yielded solutions enliven intricate mathematical structures, providing a concrete insight into the dynamics and behaviors of said equations. This paper highlights the proficiency of the generalized Kudryashov method in resolving complex issues presented by fractional differential equations. Our study not only broadens the range of mathematical methods but also enhances our comprehension of the intriguing realm of nonlinear physical phenomena.Öğe On an axiomatization of the grey Banzhaf value(Amer Inst Mathematical Sciences-Aims, 2023) Ekici, MustafaThe Banzhaf value with grey data is a solution concept in cooperative grey games that has been extensively studied in the context of operations research. The author aims to define the traits of the Banzhaf value in cooperative grey games, where the values of coalitions are depicted as grey numbers within intervals. The grey Banzhaf value is defined by several axioms, including the grey dummy player, grey van den Brink fairness, and grey superadditivity. By presenting these axioms, this investigation contributes novel insights to the axiomatic characterization of the grey Banzhaf value, offering a distinct perspective. Finally, the study concludes by presenting applications in cooperative grey game models, thereby enriching the understanding of this concept.Öğe On solving the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation by using two efficient method(Süleyman Demirel University, 2025) Ekici, MustafaThis paper employs two distinct yet potent methodologies in order to tackle the intricate difficulties posed by nonlinear partial differential equations. Our primary focus is on deriving novel exact solutions for the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation. The (3+1)-dimensional B-type Kadomtsev-Petviashvili equation serves as the focal point of this research. By employing the unified method and the generalized Kudryashov method, solitary wave solutions for this equation are obtained. These methods not only contribute to the theoretical analysis of nonlinear systems but also facilitate a deeper understanding of multidimensional wave phenomena. The newly derived exact solutions provide significant insights into the physical interpretations of these equations, paving the way for advanced applications in fields such as energy transmission, signal processing, and wave dynamics. This work highlights the effectiveness of these methodologies and their potential to enhance both the theoretical and practical understanding of nonlinear phenomenaÖğe Travelling Wave Solutions for Some Time-Fractional Nonlinear Differential Equations(2024) Ekici, MustafaThis study employs the powerful generalized Kudryashov method to address the challenges posed by fractional differential equations in mathematical physics. The main objective is to obtain new exact solutions for three important equations: the (3+1)-dimensional time fractional Jimbo-Miwa equation, the (3+1)-dimensional time fractional modified KdV-Zakharov-Kuznetsov equation, and the (2+1)-dimensional time fractional Drinfeld-Sokolov-Satsuma-Hirota equation. The generalized Kudryashov method is highly versatile and effective in addressing nonlinear problems, making it a pivotal component in our research. Its adaptability makes it useful in diverse scientific disciplines. The method simplifies complex equations, improving our analytical capabilities and deepening our understanding of system dynamics. Additionally, we define fractional derivatives using the conformable fractional derivative framework, providing a strong foundation for our mathematical investigations. This paper examines the effectiveness of the generalized Kudryashov method in solving complex challenges presented by fractional differential equations and aims to provide guidance for future studies.
