This work develops and analyzes a finite difference scheme for a coupled system of integro-differential equations describing the tangential flow of viscoelastic fluids governed by a generalized Maxwell model with a two-parameter Mittag-Leffler relaxation kernel. The nonlocal Mittag-Leffler memory kernel introduces significant analytical challenges in the stability and convergence analysis due to the history-dependent nature of the constitutive law. By employing a discrete energy approach together with positivity properties of the convolution kernel, we prove that the proposed numerical scheme is uniquely solvable, unconditionally stable, and convergent in a discrete weighted ℓ2-norm. Numerical experiments confirm the theoretical convergence rates for both exponential and genuine Mittag-Leffler kernels, and illustrate the influence of model parameters on the viscoelastic response.
In this paper, a class of nonconvex nonsmooth optimization problems is characterized with interval-valued objective functions with equality and inequality constraints. We establish the E-Karush-Kuhn-Tucker (E-KKT) necessary optimality conditions for such problems under the assumption of E-subdifferentiability. Also, sufficient optimality conditions are derived by employing appropriate notions of E-subconvexity. Further, we propose and analyze a l1 exact E-penalty function approach for solving constrained nondifferentiable optimization problems involving interval-valued objective functions. The exactness property of the proposed E-penalty function is thoroughly investigated in the E-subconvex case. Precise conditions are provided under which the set of LU−E-optimal solutions to the original interval-valued problem coincides exactly with the set of optimal solutions to the corresponding penalized problem. Furthermore, an implementable algorithm based on the minimization of the l1 exact E-penalty function is developed, together with a rigorous convergence analysis.
