Abstract
In this paper, we establish sufficient conditions for the existence and uniqueness of the solution for a class of initial-boundary value problems with Dirichlet condition for a class of fractional partial differential equations. The results are established by a method based on a priori estimate "energy inequality" and the Faedo-Galerkin method.
Highlights
Differential equations have a remarkable ability to predict the world around us
All of them may be described by the same second-order partial differential equation, the wave equation, which allows us to think of light and sound as forms of waves, much like familiar waves in the water
The present paper is devoted to the study of initial-boundary value problem for a parabolic equation with timefractional derivative with Dirichlet condition by Faedo-Galerkin method and a priori estimate, which has not been studied so far
Summary
Differential equations have a remarkable ability to predict the world around us. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. For example in medicine for modelling cancer growth or the spread of disease, in engineering for describing the movement of electricity, in chemistry for modelling chemical reactions and to computer radioactive half life, in economics to find optimum investment strategies, in physics to describe the motion of waves, pendulums or chaotic systems. It is used in physics with Newton’s Second Law of Motion and the Law of Cooling and in Hooke’s Law for modeling the motion of a spring or in representing models for population growth and money flow circulation. The present paper is devoted to the study of initial-boundary value problem for a parabolic equation with timefractional derivative with Dirichlet condition by Faedo-Galerkin method and a priori estimate, which has not been studied so far
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