LAUSR

Abstract This study deals with a computational scheme based on the Chebyshev cardinal wavelets for a new class of nonlinear variable-order (V-O) fractional quadratic integral equations (QIEs). Through the way, a new operational matrix (OM) of V-O fractional integration is derived for the mentioned basis functions. More precisely, the unknown solution is expanded in terms of the Chebyshev cardinal wavelets including undetermined coefficients. Thereafter, a system of nonlinear algebraic equations is extracted by substituting the mentioned expansion in the intended problem, utilizing the generated OM and considering the cardinal property of the basis functions. Finally, the approximate solution is obtained by solving the yielded system. Meanwhile, the convergence of the established approach is investigated in the Sobolev space. Moreover, the applicability and the accuracy of the method are examined by solving several numerical examples.