en عمومى General پژوهشي Research <div dir="ltr" style="text-align: justify;"><span style="font-size:11pt"><span style="line-height:normal"><span style="unicode-bidi:embed"><span sans-serif="" style="font-family:Calibri,"><span new="" roman="" style="font-family:" times="">In this paper, we introduced a distributed order time fractional Coronavirus-19 disease transmission involving Caputo-Prabhakar fractional derivative of &alpha; order in time t. The coronavirus 19 disease model has 8 inger dients leading to system of 8 nonlinear ordinary differential equations in this sense. To solve these types of equations, we proposed a numerical method based on the upon Legendre wavelets optimization approximations. In the first stage, by applying the Legendre wavelets optimization functions and Laplace transform an exact formula for the Prabhakar fractional integral operator is derived. Then, we apply this exact formula and the properties of Legendre wavelets optimization functions to change the given equation into a system of algebraic equations. We calculated the approximation optimal solutions of our system applying the Newton&rsquo;s iterative method. The optimal approximate solutions obtained by using the proposed method are considered as the best solutions for the proposed equation. Error analysis is examined to verify the practical efficiency of the proposed method. In the end, for the efficiency and performance of the proposed method, the numerical results are shown in the figure.</span></span></span></span></span><br> &nbsp;</div> COVID-19 Virus, Distributed-Order, Legendre Wavelets Optimization Approach, Caputo-Prabhakar Derivative, Error Analysis 25 42 http://ijorlu.lahijan.iau.ir/browse.php?a_code=A-10-548-1&slc_lang=en&sid=1 M. Khasteh Khasteh_math@yahoo.com 10031947532846002275 10031947532846002275 No Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran A. H. Refahi Sheikhani ah_refahi@yahoo.com 10031947532846002276 10031947532846002276 Yes Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran F. Shariffar farhadshariffar@yahoo.com 10031947532846002277 10031947532846002277 No Department of Applied Mathematics, Fouman and Shaft Branch, Islamic Azad University, Fouman, Iran