Author/Authors :
al-musalhi, fatma s. sultan qaboos university - department of mathematics, Muscat, Oman , al-salti, nasser s. sultan qaboos university - department of mathematics, fracdiff research group, Muscat, Oman , karimov, erkinjon sultan qaboos university - fracdiff research group, Muscat, Oman , karimov, erkinjon uzbekistan academy of sciences - institute of mathematics, Tashkent, Uzbekistan
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
