Abstract
A new simple well-behaved definition of the fractional derivative termed as conformable fractional derivative and introducing a geometrical approach of fractional derivatives, non-integral order initial value problems are an attempt to solve in this article. Based on the geometrical interpretation of the fractional derivatives, the solution curve is approximated numerically. Two special phenomena are employed for concave upward and downward curves. In order to obtain the solution of fractional order differential equation (FDE) with the integer-order initial condition, some new criteria on fractional derivatives are proposed.
Highlights
The impact of this fractional calculus in both pure and applied branches of science and engineering started to increase substantially during the last two decades apparently
A new geometrical approach to obtain an approximate solution of fractional order differential equation (FDE), subject to integer-order initial conditions which are significant to describe most of the physical phenomena, is the main course of study of this paper
In order to assess the applicability of the proposed method, we have considered a number of fractional differential equations with initial conditions
Summary
The impact of this fractional calculus in both pure and applied branches of science and engineering started to increase substantially during the last two decades apparently. In an endeavour to incorporate the curvature of the curve to arrive at an approximate numerical solution of the initial-value problem (1); one tries to explore the possibility of alternative approaches. This leads to the following two types of procedures:. A new geometrical approach to obtain an approximate solution of FDEs, subject to integer-order initial conditions which are significant to describe most of the physical phenomena, is the main course of study of this paper
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