The analytical solutions for conformable integral equations and integro-differential equations by conformable Laplace transform


Özkan O., Kurt A.

Optical and Quantum Electronics, vol.50, no.2, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1007/s11082-018-1342-2
  • Journal Name: Optical and Quantum Electronics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Conformable fractional derivative, Conformable integro-differential equation, Conformable Laplace transform, Integral equation
  • Hatay Mustafa Kemal University Affiliated: Yes

Abstract

In this article, existence theorem for conformable Laplace transform is expressed. Then by using basic properties of conformable Laplace transform such as convolution theorem, conformable Laplace transform of fractional derivative and fractional integral, authors obtained the exact solution of initial value problems for integral equations and integro-differential equations where the derivatives and integrals are in conformable sense. In the literature it is the first time that obtaining the solutions of integro differential equations, integral equations by means of conformable fractional derivative.