Abstract
During the past three decades or so, the widely-investigated subject of fractional calculus (that is, calculus of derivatives and integrals of any arbitrary real or complex order) has remarkably gained importance and popularity due chiefly to its demonstrated applications in numerous seemingly diverse fields of science and engineering. Recently, many problems in the physical sciences can be expressed and solved succinctly by recourse to the fractional calculus. Various problems which arise from the physical situation lead to certain classes of partial differential equations. The classical methods in obtaining solutions of the boundary value problems of mathematical physics are Fourier transform, and other integral transforms. The main object of this paper is by using the method of Fractional Calculus to get the closed solution of various engineering problems. That is we use the method of fractional calculus to solve the Partial Differential Equations, such as heat equation, and Laplace's equation.
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