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We construct λ − Wijsman density and λ − Wijsman statistical convergence (SC) on a time scale. Furthermore, strongly Wijsman λ p − summability is defined. Also, inclusion relations for sets of Wijsman statistical convergent sequences are given by considering the sequences μ Δ λ (t) and μ Δ β (t) in the classΛ on time scales. These theoretical parts are supported by some results and examples. [ABSTRACT FROM AUTHOR]

In this study, integro-differential equation under separated boundary conditions is considered. In fact, we study the inverse nodal problem, which includes differential part of Sturm–Liouville equation and Volterra type integral to obtain approximative solutions by Legendre polynomials. And, we use Legendre wavelets method to solve these types of problems. In addition, we present the error bound of q (x) for continuous derivatives with its approximative solution. Once and for all, the strength of the method can be seen in a few examples. [ABSTRACT FROM AUTHOR]

In this study, we examine the notion of Δλ-statistical boundedness on an arbitrary time scale. Moreover, some inclusion relations are obtained. [ABSTRACT FROM AUTHOR]

The p -Laplacian type Dirac systems are nonlinear generalizations of the classical Dirac systems. They can be observed as a bridge between nonlinear systems and linear systems. The purpose of this study is to consider p -Laplacian Dirac boundary value problem on an arbitrary time scale to get forceful results by examining some spectral properties of this problem on time scales. Interesting enough, the p -Laplacian type Dirac boundary value problem exhibits the classical Dirac problem on time scales. Moreover, we prove Picone's identity for p -Laplacian type Dirac system which is an important tool to prove oscillation criteria on time scales. It generalizes a classical and well-known theorem for p = 2 to general case p > 1. [ABSTRACT FROM AUTHOR]

In this study, we consider Sturm-Liouville (SL) equation under the separated boundary conditions on a finite interval. We get the approximate solutions of inverse SL problem by using different input data as eigenvalues and nodes (zeros of eigenfunctions), separately, and calculate the computed errors related to the obtained approximate solutions. To calculate the approximate solutions, we use Chebyshev interpolation technique by applying first kind of Chebyshev polynomials. Eventually, the numerical results are presented by providing some examples. [ABSTRACT FROM AUTHOR]

Boundary value problem on time scales is fairly a new subject and has great importance in mathematics. In this study, we explore an eigenvalue problem for Dirac system with separated boundary conditions on an arbitrary time scale. Recent results in the literature about spectral theory of classical Dirac system as orthogonality of eigenfunctions and simplicity of the eigenvalues are generalized and improved. Furthermore, some eigenfunction estimates of the first and second canonic forms for Dirac system are established on. These results will provide a significant contribution to the development of the spectral theory on time scales. [ABSTRACT FROM PUBLISHER]