Stability and convergence computational analysis of a new semi analytical-numerical method for fractional order linear inhomogeneous integro-partial-differential equations

The aim of this research is to develop a semi-analytical numerical method for solving fractional order linear integro partial differential equations (FOLIPDEs), particularly focusing on inhomogeneous FOLIPDEs of various types, such as fractional versions of Fredholm and Volterra type integral equations. To achieve this goal, we will explore existing fractional formulations of linear model integral equations. We will then outline of the proposed semi-analytical numerical procedure, including an analysis of its stability and convergence properties. Through specific numerical examples, we will demonstrate that this approach is not only clear and efficient but also accurate. The results obtained will indicate that this method holds significant potential for addressing a wide range of FOLIPDEs. Finally, we will summarize the contributions of this work to the advancement of semi-analytical numerical method for FOLIPDEs and discuss directions for future research in this area.