The article entitled “ A study on the existence of numerical and analytical solutions for fractional integrodifferential equations in hilfer type with simulation” based on the studies conducted by Department of Mathematics member Prof. Dr. Seher Melike Aydoğan was published in AIMS Mathematics.

Fractional derivative operators have become a famous part of modeling natural and physical phenomena. During the progress and evolution of these operators, it has become clear to researchers that each of these operators has special capacities for investigating phenomena in engineering sciences, physics, biological mathematics, etc. Fixed point theory and its famous contractions have always served as useful tools in these studies. In this regard, in this work, they considered the Hilfer-type fractional operator to study the proposed integro-differential equation. They have used the capabilities of measure theory and fixed point techniques to provide the required space to guarantee the existence of the solution. The Schauder and Arzela-Ascoli theorems play a fundamental role in the existence of solutions. Finally, they provided two examples with some graphical and numerical simulation to make our results more objective.

https://www.aimspress.com/aimspress-data/math/2023/5/PDF/math-08-05-541.pdf