General conformable fractional derivative and its physical interpretation

Cobweb model with conformable fractional derivatives

“…1. If = 1, then (16) and its solution (17) coincide with the ordinary differential equation and its solution given in Gandolfo. 2, Page 191 2.…”

“…is a constant and T (f) is the conformable fractional derivative with 0 < ≤ 1. For the cobweb model (16), expectations grow in the same manner when c > 0, ie, if the price is increasing, then producers expect a further increase, and if the price is decreasing, then producers expect a further decrease. However, when c < 0, expectations follow the opposite direction.…”

“…Consequently, conformable fractional derivatives have become popular. Recently, several articles on conformable fractional calculus and its applications to biology, physics, and engineering [9][10][11][12][13][14][15][16] have been published, but none of them deals with economics. From this point of view, we use the conformable fractional derivative to construct fractional-order cobweb models in continuous time.…”

Conformable fractional Sturm‐Liouville equation

“…Later in other work, Abdeljawad defined the right and left conformable fractional derivatives, the fractional chain rule, and fractional integrals of higher orders. Recently, this topic has attracted the attention of several scholars in various fields (see other studies) …”

“…Recently, this topic has attracted the attention of several scholars in various fields (see other studies). [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] It is well known that the Sturm-Liouville problems play an important role in many areas of science. It deals with the second-order ordinary differential equation of the form − ( p(t) ′ (t) ) ′ + q(t) (t) = (t).…”