Existence and stability results for the integrable solution of a singular stochastic fractionalorder integral equation with delay
Volume 33, Issue 1, pp 1726
http://dx.doi.org/10.22436/jmcs.033.01.02
Publication Date: November 16, 2023
Submission Date: July 12, 2023
Revision Date: August 08, 2023
Accteptance Date: September 21, 2023
Authors
A. M. A. ElSayed
 Faculty of Science, Alexandria University, Alexandria, Egypt.
M. Abdurahman
 College of Science, Taibah University, AlMadinah, Saudi Arabia.
H. A. Fouad
 Faculty of Science, Alexandria University, Alexandria, Egypt.
 College of Science, Taibah University, AlMadinah, Saudi Arabia.
Abstract
In this paper, we are concerning with the existence of the solution \( \mathfrak{V} \in L_1([0,\tau],L_2(\Omega))\) of the singular stochastic fractionalorder integral equation with delay \(\varrho(.) \),
\[
\mathfrak{V}(t) = B(t) t^{\alpha  1} + \lambda ~ \mathfrak{I}^{\beta} \mathfrak{G}(t,\mathfrak{V}(\varrho (t))), ~~~t\in (0,\tau],
\]
where \(B(t)\) is a given second order mean square stochastic process, \( \lambda \) is a parameter, \(\varrho (t) \leq t\), and \(\mathfrak{G}(t,\mathfrak{V}) \) is a measurable function in \(t \in (0,\tau]\) and satisfies Lipschitz condition on the second argument.
The HyersUlam and generalized HyersUlamRassias stability will be proved. Moreover, the continuous dependence of the solution on the process \(B(t)\) and \(\lambda\) will be studied. As applications,
some nonlocal, weighted and nonlocalweighted integral problems of stochastic fractionalorder differential equations will be studied.
Share and Cite
ISRP Style
A. M. A. ElSayed, M. Abdurahman, H. A. Fouad, Existence and stability results for the integrable solution of a singular stochastic fractionalorder integral equation with delay, Journal of Mathematics and Computer Science, 33 (2024), no. 1, 1726
AMA Style
ElSayed A. M. A., Abdurahman M., Fouad H. A., Existence and stability results for the integrable solution of a singular stochastic fractionalorder integral equation with delay. J Math Comput SCIJM. (2024); 33(1):1726
Chicago/Turabian Style
ElSayed, A. M. A., Abdurahman, M., Fouad, H. A.. "Existence and stability results for the integrable solution of a singular stochastic fractionalorder integral equation with delay." Journal of Mathematics and Computer Science, 33, no. 1 (2024): 1726
Keywords
 Stochastic fractional calculus
 singular stochastic integral equation
 stochastic fractionalorder differential equations
 existence of integrable solution
 continuous dependence
 HyersUlam stability
MSC
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