Resat Yilmazer

Explicit Solutions of Singular Differential Equation by Means of Fractional Calculus Operators

Recently, several authors demonstrated the usefulness of fractional calculus operators in the derivation of particular solutions of a considerably large number of linear ordinary and partial differential equations of the second and higher orders. By means of fractional calculus techniques, we find explicit solutions of second-order linear ordinary differential equations.

Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator

In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs). Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE) by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.

Fractional Solutions of Bessel Equation with N-Method

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N ν method, we derive the fractional solutions of the equation.

Explicit Solutions of Fractional SchröDinger Equation via Fractional Calculus Operators

In this paper, we investigate the schrodinger equation in a given  - dimensional fractional space with a columb potential depending on a parameter and obtain explicit solution of second order linear ordinary differential equation.

Discrete fractional solutions of a Legendre equation

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

Discrete fractional solutions of an associated Laguerre equation

In this article, we will give theorems for the discrete fractional solutions of the homogeneous and nonhomogeneous associated Laguerre equation by using discrete fractional nabla operator.In this article, we will give theorems for the discrete fractional solutions of the homogeneous and nonhomogeneous associated Laguerre equation by using discrete fractional nabla operator.

Particular solutions of the radial Schrödinger equation via Nabla discrete fractional calculus operator

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus (DFC) has also an important position in the fractional calculus. The nabla operator in DFC is practical for the singular differential equations. The purpose of this study is to obtain particular solutions of the radial Schrodinger equation (that is, the most important equation of quantum physics) via nabla DFC operator. These solutions were obtained in the forms of discrete fractional.

Discrete fractional solutions of the radial equation of the fractional Schrödinger equation

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus (DFC) has also an important position in the fractional calculus. The nabla operator in DFC is practical for the singular differential equations. In this study, we investigated the radial equation of the fractional Schrodinger equation. The particular solutions of this equation was obtained as discrete fractional forms via ∇-discrete fractional operator out of known methods.