Basic theory of initial value problems of conformable fractional differential equations

• Published in: Advances in difference equations Vol. 2018; no. 1; pp. 1 - 14
• Main Authors: Zhong, Wenyong, Wang, Lanfang
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 12.09.2018; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Boundary value problems; Conformable fractional derivatives; Difference and Functional Equations; Differential equations; Fixed point theorems; Fixed points (mathematics); Fractional calculus; Fractional differential equations; Functional Analysis; Initial value problems; Mathematical analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Fixed point theorems; Initial value problems; Fractional differential equations; Conformable fractional derivatives

In this paper, we discuss the basic theory of the conformable fractional differential equation T α a x ( t ) = f ( t , x ( t ) ) , t ∈ [ a , ∞ ) , subject to the local initial condition x ( a ) = x a or the nonlocal initial condition x ( a ) + g ( x ) = x a , where 0 < α < 1 , T α a x ( t ) de...