Initial and Boundary Value Problems for Fractional differential equations involving Atangana-Baleanu Derivative

Initial value problem involving Atangana-Baleanu derivative is considered. An Explicit solution of the given problem is obtained by reducing the differential equation to Volterra integral equation of second kind and by using Laplace transform. To find the solution of the Volterra equation, the succe...

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Bibliographic Details
Published in:arXiv.org 2017-06
Main Authors: Fatma Al-Musalhi Nasser Al-Salti, Karimov, Erkinjon
Format: Article
Language:English
Subjects:
Boundary value problems
Differential equations
Laplace transforms
Series expansion
Volterra integral equations
Online Access:Get full text
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Summary:Initial value problem involving Atangana-Baleanu derivative is considered. An Explicit solution of the given problem is obtained by reducing the differential equation to Volterra integral equation of second kind and by using Laplace transform. To find the solution of the Volterra equation, the successive approximation method is used and a lemma simplifying the resolvent kernel has been presented. The use of the given initial value problem is illustrated by considering a boundary value problem in which the solution is expressed in the form of series expansion using orthogonal basis obtained by separation of variables.
ISSN:2331-8422