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Global Existence and Ulam–Hyers Stability of Ψ–Hilfer Fractional Differential Equations
Kishor Deoman Kucche,Jyoti Pramod Kharade 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.3
In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam–Hyers and Ulam–Hyers–Rassias stabilities of the Cauchy–type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using ε- approximated solutions. Finally, we present examples to illustrate our main results.