A study on the fuzzy parabolic Volterra partial integro-differential equations

Abstract

This paper is concerned with aspects of the analytical fuzzy solutions of the parabolic Volterra partial integro-differential equations under generalized Hukuhara partial differentiability and it consists of two parts. The first part of this paper deals with aspects of background knowledge in fuzzy mathematics, with emphasis on the generalized Hukuhara partial differentiability. The existence and uniqueness of the solutions of the fuzzy Volterra partial integro-differential equations by considering the type of [gH - p]-differentiability of solutions are proved in this part. The second part is concerned with the central themes of this paper, using the fuzzy Laplace transform method for solving the fuzzy parabolic Volterra partial integro-differential equations with emphasis on the type of [gH - p]-differentiability of solution. We test the effectiveness of method by solving some fuzzy Volterra partial integro-differential equations of parabolic type.