In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing a new operator. This derivative combines two known operators: respect to another function. The main results of paper are necessary sufficient optimality conditions for different types problems. Since generalized derivatives, from some well-known can be obtained as partic...

In this paper, we propose the fractal (2 + 1)-dimensional Zakharov–Kuznetsov equation based on He’s derivative for first time. The generalized variational formulation is established by using semi-inverse method and two-scale theory. obtained principle important since it not only reveals structure of traveling wave solutions but also helps us study symmetric finding paper will contribute to symm...

In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...

Abstract In this article, we formulate a model describing the evolution of thickness grounded shallow ice sheet. The sheet is constrained to be nonnegative. This renders problem under consideration an obstacle problem. A rigorous analysis shows that thus governed by set variational inequalities involve nonlinearities in time derivative and elliptic term, it admits solutions, whose existence est...

We develop a new technique to mathematically analyze and numerically simulate the weak periodic solution class of semilinear parabolic equations with discontinuous coefficients. reformulate our problem into minimization via least-squares cost function. By using variational calculus theory, we establish existence an optimal based on Lagrangian method, calculate derivative To illustrate validity ...