AUG Repository

Methods of Integral Transform for Solving some Differential Equations of Fractional Order

 dc.contributor.author محمد اسماعيل يوسف ابو عبيد dc.date.accessioned 6/12/2020 dc.date.accessioned 6/12/2020 dc.date.accessioned 2021-01-08T19:06:44Z dc.date.available 6/12/2020 dc.date.available 2021-01-08T19:06:44Z dc.date.issued 1/27/2015 dc.identifier.uri http://dspace.alazhar.edu.ps/xmlui/handle/123456789/2358 dc.description.abstract Fractional differential equations, which have derivatives of non-integer order, are very successful in describing natural and physical phenomenon like anomalous kinetics, transport, and chaos. To obtain the exact solutions of these equations, integral transforms are successful used . In this thesis , we investigate the following items : 1) we discuss the analytical solution of three kinds of the diffusion equation. The standard diffusion equation , the so-called time-fractional diffusion equation with Caputo sense and fractional diffusion equation with Caputo sense and Weyl derivative. 2) we defined the so-called time-fractional telegraph equation with Caputo sense and Weyl derivative then we derive the analytical solution for three basic problems. The whole-space domain and half-space domain problems are solved by applying the Laplace and Fourier transforms in variables t and x , respectively. The bounded space domain problem is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series. 3) we defined the so-called time-fractional evolution equation with Caputo sense and Weyl derivative then we derive the fractional Green function to obtain the analytical solutions of the time-fractional wave equation , linearized time-fractional Burgers equation and linear time-fractional KdV equation . en_US dc.language.iso en_US en_US dc.publisher Batch2 en_US dc.title Methods of Integral Transform for Solving some Differential Equations of Fractional Order en_US dc.type Thesis en_US
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