Submission is open for November 2024, Call for papers Volume 06, Issue 11, November 2024, Open Access; Peer Reviewed Journal; Fast Publication. The Journal is welcoming original Research Articles, Book Reviews, Commentaries, Reviewed Articles, Technical Notes Please you can reach us if you have any queries send email to: editor@journalijisr.com

FRACTIONAL DIFFERENTIAL EQUATIONS AND FRACTIONAL SEMIGROUPS OF OPERATORS

×

Error message

  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Notice: Trying to access array offset on value of type int in element_children() (line 6609 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
  • Deprecated function: implode(): Passing glue string after array is deprecated. Swap the parameters in drupal_get_feeds() (line 394 of /home3/ijcsrd79/public_html/journalijisr.com/includes/common.inc).
Author: 
*Amany M. Moter
Country: 
Iraq
Volume & Issue: 
Volume 06, Issue 04, April 2024
Page No: 
6250-6253
Abstract: 

In this paper, the authors investigate the solution of a second-order fractional differential equation. They consider cases where either the variable u or v is missing. The paper also introduces the concept of a fractional semigroup of operators. This involves a mapping that represents bounded linear operators on a Banach space U. The one-parameter semigroup satisfies certain properties, such as the semigroup property and having an identity operator at y = 0. The derivative of this semigroup at y = 0 is called the infinitesimal generator. The main objective of the paper is to explore the fundamental properties of these fractional semigroups and their connection to the fractional derivative of the semigroup at y = 0. We confirm that we are using the definition of Al-Sharif and Malkawi [22] for the conformable fractional derivative.

KeyWords: 
conformable fractional derivative, fractional β−semigroup, c0 − semigroup, β − infinitesimal generator.