Conformable fractional hyper geometric equation

Iman Aldarawi

doi:10.28919/jsta/3596

Abstract

In this paper we study the fractional power series solution around the regular singular point x = 0 of the conformable fractional hyper geometric differential equation. Then, we compare such solutions with that of the corresponding ordinary differential equation.

Highlights

In this paper we study the fractional power series solution around the regular singular point x = 0 of the conformable fractional hyper geometric differential equation
The subject of fractional derivative is as old as calculus
Many researchers have been trying to generalize the concept of the usual derivative to fractional derivatives

Summary

Introduction

The subject of fractional derivative is as old as calculus. In 1659, L’Hospital asked if the expression d0.5 dt 0.5 f has any meaning. (2) All fractional derivatives don’t satisfy the known product rule: Dαa ( f g) = f Dαa (g) +. All fractional derivatives don’t satisfy the known quotient rule:. (4) All fractional derivatives don’t satisfy the chain rule: Dαa ( f ◦ g) = f α g(t)gα (t). (5) All fractional derivatives don’t satisfy: Dα Dβ f = Dα+β f in general (6) Caputo definition assumes that the function f is differentiable. In [2], a new definition called conformable fractional derivative was introduced. We list here the fractional derivatives of certain functions, for the purpose of comparing the results of the new definition with the usual definition of the derivative:. Throughout this paper, we let Dα y denoted the conformable fractional derivative of y, where α ∈ The second αderivative of y will be denoted by D2α y

The main result

Some Applications