Initial and Boundary Value Problems for Fractional Differential Equations Involving Atangana-Baleanu Derivative
Al-Musalhi Fatma S.Sultan Qaboos University, P.O. Box 36, PC 123, Al Khodh, Muscat, Sultanate of OmanAl-Salti Nasser S.Sultan Qaboos University, P.O. Box 36, PC 123, Al Khodh, Muscat, Sultanate of OmanErkinjon KarimovFracDiff Research Group, Sultan Qaboos University, Muscat, Sultanate of Oman; Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent 170, Uzbekistan
Maǧallaẗ ǧāmiʿaẗ al-Sulṭān Qābūs li-l-ʿulūm/Sultan Qaboos University journal for sciencejournal2018en
ABI
Annotatsiya
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.
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