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arXiv · 1807.10105

Global Existence and Ulam--Hyers Stability of $\Psi$--Hilfer Fractional Differential Equations

Kishor D. Kucche·Jyoti P. Kharade
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Abstract

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving $\Psi$-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam--Hyers and Ulam--Hyers--Rassias stability of Cauchy--type problem is investigated via successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and uniqueness via $\epsilon$-approximated solution. An example is provided to illustrate the results we obtained.

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Kishor D. Kucche, Jyoti P. Kharade. 2018-07-26. Global Existence and Ulam--Hyers Stability of $\Psi$--Hilfer Fractional Differential Equations. https://doi.org/10.5666/kmj.2020.60.3.647

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