Research Article FractionalConformableStochasticIntegrodifferentialEquations: Existence, Uniqueness, and Numerical Simulations Utilizing the Shifted Legendre Spectral Collocation Algorithm Haneen Badawi, 1 Nabil Shawagfeh, 1 and Omar Abu Arqub 2 1 Department of Mathematics, Faculty of Science, Te University of Jordan, Amman 11942, Jordan 2 Department of Mathematics, Faculty of Science, Al•Balqa Applied University, Salt 19117, Jordan Correspondence should be addressed to Omar Abu Arqub; o.abuarqub@bau.edu.jo Received 8 September 2022; Accepted 31 October 2022; Published 28 November 2022 Academic Editor: Kazem Nouri Copyright © 2022 Haneen Badawi et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Teoretical and numerical studies of fractional conformable stochastic integrodiferential equations are introduced in this study. Herein, to emphasize the solution’s existence, we provide proof based on Picard iterations and Arzela−Ascoli’s theorem, whilst the proof of the uniqueness mainly depends on the famous Gronwall’s inequality. Also, we introduce the basic concepts related to shifted Legendre orthogonal polynomials which are utilized to be the basic functions of the spectral collocation algorithm to obtain approximate solutions for the mentioned equations that are not easy to be solved analytically. Te substantial idea of the proposed algorithm is to transform such equations into a system containing a fnite number of algebraic equations that can be treated using familiar numerical methods. For computational aims, we make a suitable discretization to evaluate the values of the Brownian motion, the noise term considered in our problem, at specifc points. In addition, the feasibility and efciency of the proposed algorithm are proved through convergence analysis and mathematical examples. To exhibit the mathematical sim• ulation, graphs and tables are lucidly shown. Obviously, the physical interpretation of the displayed graphics accurately describes the behavior of the solutions. Despite the simplicity of the presented technique, it produces accurate and reasonable results as notarized in the conclusion section. 1.Introduction Recently, greater growth of fractional calculus has been developed by many researchers. Since several real•world phenomena in assorted felds of science are represented successfully via models involving fractional derivatives, mathematicians have focused their attention on doing their best to make deeper studies that improve this branch of calculus and its properties. Te mathematicians constructed a variety of defnitions of fractional derivative operators with their associated integral inverses together with several im• portant related theories. For example, Hadamard [1] sug• gested a new approach to fractional derivatives, Khalil et al. [2] constructed the CFD and presented some related the• ories, Caputo and Fabrizio [3] developed a fractional derivative defnition that avoids singularity, and Atangana and Baleanu [4] provided the fractional ABC derivative and discussed its properties. In this regard, authors have employed fractional models for various problems. Ahmed et al. [5] built a fractional•order model to describe cancer with two immune efectors. Rihan [6] was concerned with modeling biological systems in fractional models. Xu [7] constructed a fractional model of the Volterra type of population growth. Debnath [8] sheds light on fractional calculus applications concerning engineering and science with numerical solutions to fractional problems of particular types. Te well•posedness and the simulated solutions of the FDEs occupy a great status in applied analysis and engi• neering applications. For complicated problems that have no exact analytic solutions, various operative numerical Hindawi Mathematical Problems in Engineering Volume 2022, Article ID 5104350, 21 pages https://doi.org/10.1155/2022/5104350