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Dec 30, 2018
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Dec 30, 2018
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Abstract

In the present work, an initial value problem involving the Atangana-Baleanu derivative is considered. An explicit solution of the given problem in integral form is obtained by using the Laplace transform. 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 a series expansion using an orthogonal basis obtained by separation of variables. Some examples are also given to illustrate the obtained results.

Keywords

Atangana-Baleanu derivative Initial-Boundary value problem Fractional differential equation

Article Details

Author Biographies

Al-Musalhi Fatma S., Sultan Qaboos University, P.O. Box 36, PC 123, Al Khodh, Muscat, Sultanate of Oman

Department of Mathematics

Al-Salti Nasser S., Sultan Qaboos University, P.O. Box 36, PC 123, Al Khodh, Muscat, Sultanate of Oman; 2FracDiff Research Group, Sultan Qaboos University, Muscat, Sultanate of Oman

Department of Mathematics

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