EXAMINE NEW RESULTS OF VOLTERRA FREDHOLM INTEGRO-DIFFERENTIAL EQUATION VIA CAPUTO-HADAMARD TYPE

Abstract

The objective of this study is to explore a new class of the Caputo-Hadamard fractional Volterra Fredholm integro-differential equation (Caputo-Hadamard fractional-VFIDE).The main contributions include establishing and deriving sufficient conditions for the existence, and uniqueness of solutions for the proposed VFIDE-based Caputo-Hadamard. Thestudy employs the Banach contraction mapping principle and the Krasnoselskii's alternativeto ensure the well-posedness of the system and presents a detailed mathematical analysis todiscuss the approximate solution of the proposed problem by using the modified Adomian decomposition method (ADM). To enhance the comprehension of the findings, concrete example is provided to showcase the versatility and practical applicability of the VFIDE-based Caputo-Hadamard, highlighting the novelty and potential impact of this research.