Some important results for the conformable fractional stochastic pantograph differential equations in the L p space
Year: 2024
Type: article
Abstract: Important mathematical topics include existence, uniqueness, continuous dependency, regularity, and the averaging principle. In this research work, we establish these results for the conformable fractional stochastic pantograph differential equations (CFSPDEs) in \(\mathbf{L}^{\mathrm{p}}\) space. The situation of \(\mathrm{p}=2\) is generalized by the obtained findings. First, we establish the existence and uniqueness results by applying the contraction mapping principle under a suitably weighted norm and demonstrating the continuous dependency of solutions on both the initial values and fractional exponent \(\phi\). The second section is devoted to examining the regularity of time. As a result, we find that, for each \(\Phi\in(0,\phi-\frac{1}{2})\), the solution to the considered problem has a \(\Phi\)-Hölder continuous version. Next, we study the averaging principle by using Jensen's, Grönwall-Bellman's, Hölder's, and Burkholder-Davis-Gundy's inequalities. To help with the understanding of the theoretical results, we provide three applied examples at the end.
Authors: M. I. Liaqat, F. Ud Din, A. Akgul, M. B. Riaz
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402556790