Advanced Mathematical Models & Applications

Many mathematicians are often interested in establishing the existence and uniqueness of solutions, as well as finding exact or approximate solutions, for various classes of integral and differential equations, including their fractional variants with initial or boundary conditions. Fixed point theorems serve as useful and powerful tools for addressing such problems. In this paper, the notion of a strongly sequential S-metric space is first introduced as a new generalization of S_b -metric spaces and S^JS-metric spaces. Several fixed point results for S-JS-Hardy-Rogers-type contractions and other types of contractions are obtained. To confirm the validity of these results, an illustrative application is provided, demonstrating the existence and uniqueness of a solution for a second-order boundary value differential equation, which arises in many engineering applications.