Nonlocal Telegraph Equation in Frame of the Conformable Time-Fractional Derivative

Abstract

We use the cosine family of linear operators to prove the existence, uniqueness, and stability of the integral solution of a nonlocal telegraph equation in frame of the conformable time-fractional derivative. Moreover, we give its implicit fundamental solution in terms of the classical trigonometric functions.

Improvement on Conformable Fractional Derivative and Its Applications in Fractional Differential Equations

“…Second, the conformable derivative bring us a lot of convenience when it is applied for modelling many physical problems, because the differential equations with conformable fractional derivative are easier to solve numerically than those associated with the Riemann-Liouville or Caputo fractional derivative. In fact, many researchers have already applied conformable fractional derivative to many fields and a lot of corresponding techniques were developed [13][14][15][16][17][18][19][20].…”

Nonlocal Conformable-Fractional Differential Equations with a Measure of Noncompactness in Banach Spaces

“…is new fractional derivative quickly becomes the subject of many contributions in several areas of science [11][12][13][14][15][16][17][18][19][20][21][22]. Motivated by the better effect of the fractional derivative and simple properties of the conformable fractional derivative, we consider model (1) in the framework of conformable fractional calculus.…”

Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems

“…is novel fractional derivative is very easy and satisfies all the properties of the standard one. In short time, many studies and discussion related to conformable fractional derivative have appeared in several areas of applications [1][2][3][4][5][6][7][8][9][10].…”