Abstract
We know that the solution of partial differential equations by analytical method is better than the solution by approximate or series solution method. In this paper, we discuss the solution of linear and non-linear fractional partial differential equations involving derivatives with respect to time or space variables by converting them into the partial differential equations of integer order. Also we develop an analytical formulation to solve such fractional partial differential equations. Moreover, we discuss the method to solve the fractional partial differential equations in space as well as time variables simultaneously with the help of some examples.
Highlights
The theory of fractional derivation has known great importance in mathematical research from last few decades
Sababhed. [9], came up with an idea that extends the limit definition of the derivative. He derived some results of fractional derivative by using his new definition of fractional derivative
As this definition satisfies some classical and fundamental properties [See [4, 11]] of a fractional derivative and many new researchers are taking deep interest to develop the theory of fractional derivative by using this definition of conformable fractional derivative
Summary
The theory of fractional derivation has known great importance in mathematical research from last few decades. The most used definitions of fractional derivation are Caputo definition [15] and Riemann Liouville [15] These fractional derivatives do not provide some properties of algebra of derivative and Mean Value Theorems. Odzijewicz [2] introduced different definition of the fractional derivative He discussed some important results by using his definition of fractional derivative. Katugampola [6], introduced the idea of fractional derivative by using his new definition. As this definition satisfies some classical and fundamental properties [See [4, 11]] of a fractional derivative and many new researchers are taking deep interest to develop the theory of fractional derivative by using this definition of conformable fractional derivative.
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