含Atangana-Baleanu导数的分数阶微分方程的初边值问题
Initial and Boundary Value Problems for Fractional differential equations involving Atangana-Baleanu Derivative
摘要：
考虑了含Atangana-Baleanu导数的初值问题.通过将微分方程化为第二类Volterra积分方程，并利用拉普拉斯变换，得到了问题的显式解。为了求Volterra方程的解，使用了逐次逼近方法，并给出了简化预解核的引理。通过考虑一个边值问题来说明给定初值问题的使用，在该边值问题中，解以使用通过分离变量获得的正交基的级数展开的形式表示。
英文摘要：
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.
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