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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|2020.09|Kyungpook Mathematical Journal|제60권 제3호|pp. 647-671|DOI 10.5666/KMJ.2020.60.3.649

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참고문헌

키워드

successive approximationsexistence and uniquenessΨ–Hilfer fractional derivativeUlam–Hyers stabilityε−approximate solutiondependence of solution
주제분류수학

초록

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.

Abstract

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.

참고문헌 (18)

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