Existence and Uniqueness Study of the Conformable Laplace Transform

Abstract

This paper tackles the topic of conformable Laplace transform. The authors aim at discussing its existence by exploring and providing the kind of functions that possess a conformable Laplace transform. Furthermore, the comparison theorem of conformable improper integrals is presented to further explain and justify the existence of conformable Laplace transform for some functions. The uniqueness is also established in order to determine the inverse of conformable Laplace transform for functions. Moreover, we present a table of the conformable Laplace transform of the usual functions. Finally, as an application, we use the conformable Laplace transform for solving some fractional differential equations.

A Semi‐Analytical Solution of Inverse Laplace Transform

“…is is useful when the exact solution is unknown. For many engineering problems [18][19][20][21][22][23], medicine problems [24], and integro-differential equations of second-order problems [25][26][27], this method might be useful.…”

The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems

“…Theorem 1 (see [33]). Let f t be piecewise continuous on t ≥ 0 and have a conformable exponential order at infinity with f t ≤ ME a, t for t ≥ C. Then, the conformable Laplace transform L α f t s exists for s > a.…”