Abstract
In this paper, we are interested in the study of a Caputo time fractional advection–diffusion equation with nonhomogeneous boundary conditions of integral types ∫01vx,tdx and ∫01xnvx,tdx. The existence and uniqueness of the given problem’s solution is proved using the method of the energy inequalities known as the “a priori estimate” method relying on the range density of the operator generated by the considered problem. The approximate solution for this problem with these new kinds of boundary conditions is established by using a combination of the finite difference method and the numerical integration. Finally, we give some numerical tests to illustrate the usefulness of the obtained results.
Highlights
Fractional Partial Differential Equations (FPDEs) have become very important in recent years due to their use in several mathematical models
FPDEs are considered as the generalization of a partial differential equation (PDE) of an integer order of an arbitrary order
Due to the properties of Fractional Differential Equations (FDE), different models are created for complex phenomena using FPDEs, for example, in electroanalytical chemistry, viscoelasticity [1,2], porous environment, fluid flow, thermodynamic [3,4], diffusion transport, rheology [5,6,7], electromagnetism, signal processing [8], electrical network [9] and others [10,11,12]
Summary
Fractional Partial Differential Equations (FPDEs) have become very important in recent years due to their use in several mathematical models. Several problems have been mentioned in modern physics and technology using partial differential equations where the nonlocal conditions are described by integrals as. These integral conditions are of great interest due to their applications in many fields: In population dynamics, heat diffusion–advection, models of blood circulation, chemical engineering thermoelasticity [16]. F Liu [24,25], El-Nabulsi, R.A [26,27,28] and others [29,30,31,32,33] Among these authors we can cite Yuriy Povstenko [34] who studied the time fractional diffusion-wave equation with classic boundary conditions. All numerical and graphical results obtained are produced using MATLAB software
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