Weakly Singular Wendroff-Type Integral Inequalities of Multiple Variables with Multiple Nonlinear Terms and Their Applications

This paper systematically studies a class of weakly singular Wendroff-type integral inequalities with multiple variables and multiple nonlinear terms. We establish explicit bounds for the unknown functions by utilizing the method of characteristic functions and mathematical induction. These results generalize and improve existing inequalities found in the literature. Furthermore, we apply them to fractional partial differential equations to study the uniqueness, boundedness, and continuous dependence of solutions. Even in the presence of singularities, the proposed method proves effective. An application example is provided to illustrate the validity of the main results.