Browsing by Author "Sevli, Hamdullah"

Now showing 1 - 14 of 14

An Approximation Property of Gaussian Functions
(Texas State Univ, 2013) Jung, Soon-Mo; Sevli, Hamdullah; Sevgin, Sebaheddin
Using the power series method, we solve the inhomogeneous linear first order differential equation y'(x) + lambda(x - mu)y(x) = Sigma(infinity)(m = 0) a(m) (x - mu)(m), and prove an approximation property of Gaussian functions.
Extending Dirac and Faddeev-Jackiw Formalisms To Fractal First Α-Order Lagrangian Systems
(Springer Basel Ag, 2025) Golmankhaneh, Alireza Khalili; Sevli, Hamdullah; Tavares, Dina; Jorgensen, Palle E. T.
This paper presents the foundational concepts of fractal calculus before generalizing the Dirac Constraint Formalism and the Faddeev-Jackiw Formalism for first alpha-order Lagrangian systems in fractal spaces with non-integer dimensions. We provide a detailed analysis of the generalization process, highlighting the theoretical framework and key results, including the extended structure of the constraint systems in these Lagrangian formulations. Specific examples are discussed to demonstrate the practical application of the generalized formalism and to validate the consistency of our results. Moreover, graphical visualizations are included to enhance clarity, offering a visual interpretation of the findings and illustrating the relationship between the theory and its real-world implications.
Fractal Hankel Transform
(Mdpi, 2025) Golmankhaneh, Alireza Khalili; Sevli, Hamdullah; Cattani, Carlo; Vidovic, Zoran
This paper explores the extension of classical transforms to fractal spaces, focusing on the development and application of the Fractal Hankel Transform. We begin with a concise review of fractal calculus to set the theoretical groundwork. The Fractal Hankel Transform is then introduced, along with its formulation and properties. Applications of this transform are presented to demonstrate its utility and effectiveness in solving problems within fractal spaces. Finally, we conclude by summarizing the key findings and discussing potential future research directions in the field of fractal analysis and transformations.
General Absolute Summability Factor Theorems Involving Quasi-Power Sequences
(Pergamon-elsevier Science Ltd, 2009) Sevli, Hamdullah
In this paper a general theorem concerning the vertical bar A, delta vertical bar(k) summability methods has been proved, which generalizes two results of Sevli and Leindler [H. Sevli and L. Leindler, n the absolute summability factors of infinite series involving quasi-power-increasing sequences, Computers and Mathematics with Applications 57 (2009), 702-709]. We obtain sufficient conditions for Sigma a(n)lambda(n) to be summable vertical bar A, delta vertical bar(k), k >= 1, 0 <= delta < 1/k, by using quasi-power- increasing sequences. (C) 2009 Elsevier Ltd. All rights reserved.
Generalized Hausdorff Matrices as Bounded Operators Over Ak
(Eudoxus Press, Llc, 2009) Savas, Ekrem; Sevli, Hamdullah
In this paper we prove a theorem which shows that a generalized Hausdorff matrix is a bounded operator on A(k), defined below by (2); i.e., (H-beta, mu) is an element of B (A(k))
Hyers-Ulam Stability on Local Fractal Calculus and Radioactive Decay
(Springer Heidelberg, 2021) Golmankhaneh, Alireza Khalili; Tunc, Cemil; Sevli, Hamdullah
In this paper, we summarize the local fractal calculus, called F-alpha-calculus, which defines derivatives and integrals of functions with fractal domains of non-integer dimensions, functions for which ordinary calculus fails. Hyers-Ulam stability provides a method to find approximate solutions for equations where the exact solution cannot be found. Here, we generalize Hyers-Ulam stability to be applied to oi-order linear fractal differential equations. The nuclear decay law involving fractal time is suggested, and it is proved to be fractally Hyers-Ulam stable.
Mean Ergodic Theorems for Power Bounded Measures
(Academic Press inc Elsevier Science, 2021) Mustafayev, Heybetkulu; Sevli, Hamdullah
Let G be a locally compact abelian group and let M(G) be the convolution measure algebra of G. A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0) parallel to mu(n)parallel to(1) < infinity, where mu(n) denotes nth convolution power of mu. We show that if mu is an element of M(G) is power bounded and A = [a(n,k)](n,k=0)(infinity) is a strongly regular matrix, then the limit lim(n ->infinity) Sigma(infinity)(k=0) a(n,k) mu(k) exists in the weak* topology of M(G) and is equal to the idempotent measure theta, where (theta) over cap = 1(int)F(mu). Here, (theta) over cap is the Fourier-Stieltjes transform of theta, F-mu :={gamma is an element of Gamma : (mu) over cap(gamma) = 1}, and 1(int) F-mu is the characteristic function of int F-mu. Some applications are also given. (C) 2021 Elsevier Inc. All rights reserved.
On Absolute Cesaro Summability
(Springer international Publishing Ag, 2009) Sevli, Hamdullah; Savas, Ekrem
Denote by A(k) the sequence space defined by A(k) = {(s(n)) : Sigma(infinity)(n=1) n(k-1)vertical bar a(n)vertical bar(k) < infinity, a(n) = s(n) - s(n-1)} for k >= 1. In a recent paper by E. Savas, and H. Sevli (2007), they proved every Cesaro matrix of order alpha, for alpha > - 1, (C, alpha) is an element of B(A(k)) for k >= 1. In this paper, we consider a further extension of absolute Cesaro summability. Copyright (C) 2009 H. Sevli and E. Savas.
On Extension of a Result of Flett for Cesaro Matrices
(Pergamon-elsevier Science Ltd, 2007) Savas, Ekrem; Sevli, Hamdullah
In this work we prove a theorem which shows that a Cesaro matrix of order alpha > -1 is a bounded operator on A(k), defined below by (2); i.e., (C, alpha) is an element of B (A(k)). (C) 2006 Published by Elsevier Ltd.
On Initial Value Problems of Fractal Delay Equations
(Elsevier Science inc, 2023) Golmankhaneh, Alireza Khalili; Tejado, Ines; Sevli, Hamdullah; Valdes, Juan E. Napoles
In this paper, we give a brief summary of fractal calculus. Fractal functional differential equations are formulated as a framework that provides a mathematical model for the phe-nomena with fractal time and fractal structure. Fractal retarded, neutral, and renewal delay differential equations with constant coefficients are solved by the method of steps and us-ing Laplace transform. The graphs of solutions are given to show the details.(c) 2023 Elsevier Inc. All rights reserved.
On the Instability of Solutions of Certain Fifth Order Nonlinear Differential Equations
(Georgian Natl Acad Sciences, 2005) Tunc, Cemil; Sevli, Hamdullah
The main purpose of this paper is to give sufficient conditions which guarantee the instability of the trivial solution of a nonlinear vector differential equation as follows: X-(5) + psi((X) over dot,<(X)double over dot>)(X) triple over dot + (phi)(X,(X) over dot ,<(X)double over dot>) + circle minus(X) over dot + F(X) 0.
On the Perturbation of Volterra Integro-Differential Equations
(Pergamon-elsevier Science Ltd, 2013) Jung, Soon-Mo; Sevgin, Sebaheddin; Sevli, Hamdullah
In this work, we will prove that every solution of a perturbed Volterra integro-differential equation can be approximated by a solution of the Volterra integro-differential equation. (C) 2013 Elsevier Ltd. All rights reserved.
Razumikhin Qualitative Analyses of Volterra Integro-Fractional Delay Differential Equation With Caputo Derivatives
(Elsevier, 2021) Graef, John R.; Tunc, Cemil; Sevli, Hamdullah
A non-linear system of Volterra integro-fractional delay differential equations with Caputo fractional derivatives is considered. New sufficient conditions for uniform stability, asymptotic stability, and Mittag-Leffler stability of the zero solution of the unperturbed system, and the boundedness of all solutions of the perturbed system, are presented. The technique of proof involves the Razumikhin method with an appropriate Lyapunov function. For illustrative purposes, two examples are provided. (C) 2021 Published by Elsevier B.V.
Stability and Boundedness Properties of Certain Second-Order Differential Equations
(Pergamon-elsevier Science Ltd, 2007) Tunc, Cemil; Sevli, Hamdullah
In this paper, we investigated the differential equation X A(t)F(X) = P(t, X, X) in two cases; (a) P = 0 and (b) P not equal 0. For the case (a), the stability of the solution X = 0 and the uniform boundedness of all solutions of this equation are investigated; in the case (b) the boundedness of all solutions of the same equation is discussed. (c) 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.