Abstract
This paper deals with Cauchy problems and nonlocal problems for non-linear Stieltjes differential equations corresponding to a certain function g. We establish existence and uniqueness results for nonlinear equations with initial value or nonlocal conditions in the space ℬ𝒞 g ([0, H], ℝ) using fixed point methods and g-topology theory. We introduce the concepts of Ulam-Hyers (UH) and generalized Ulam-Hyers-Rassias (UHR) stability and present Ulam type stability results for linear and nonlinear equations in the spaces 𝒜𝒞 g ([0, H], ℝ) ⊂ ℬ𝒞 g ([0, H], ℝ) and ℬ𝒞 g ([0, H], ℝ). Finally, numerical examples are given to illustrate our results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
