Solving Volterra fuzzy integro-differential equations using fuzzy Elzaki transform homotopy perturbation method

Fuzzy integro-differential equations are used for modeling real-life phenomena that involve uncertain (fuzzy) parameters or variables. The combination of the fuzzy Elzaki transform and homotopy perturbation method provides a powerful hybrid technique for solving fuzzy integro-differential equations. Therefore, the aim of this paper is to modify and apply a new hybrid method called fuzzy Elzaki transform homotopy perturbation method for the first time in literature to solve fuzzy integro-differential equations. In particular, the fuzzy Elzaki transform homotopy perturbation method is developed and applied for solving linear and non-linear second-kind fuzzy Volterra integro-differential equations, and non-linear second kind fuzzy mixed Fredholm- Volterra integro-differential equations. Finally, several examples are presented to show that the fuzzy Elzaki transform homotopy perturbation method is efficient for solving wide types of fuzzy integro-differential equations with high accuracy. The novelty of this work lies in its ease of use and its high efficiency, which allows mathematicians to obtain reliable results under fuzzy Hukuhara differentiability aspects in a short time.