The local fractional variational iteration method is applied to a modified Fisher?s equation defined on Cantor sets with the fractal conditions. solution process simple, and accuracy of approximate high. provides an unrivaled tool for differential equations. Key word: equation, analytical solutions, method, derivative

Four fractal nonlinear oscillators (The Duffing oscillator, attachment Toda and a oscillator) are successfully established by He’s derivative in space, their variational principles obtained semi-inverse transform method. The approximate frequency of the four found simple formula. results show formula is powerful tool to class oscillators.

This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which—being certainly of independent interest...

The convection-diffusion process in porous electrodes depends greatly upon the structure. A fractal model for catalyst a thin-zone bed reactor is established using He?s derivative, and variational principle also space, an approximate solution obtained. Additionally ancient Chinese algorithm adopted to solve algebraic equation.

In this article, we mainly consider a modification of the high-order long water-wave equation with unsmooth boundaries by adopting new fractal derivative. Its variational principles are successfully constructed semi-inverse method, obtained helpful to study symmetry, discover conserved quantity, and have wide applications in numerical simulation.

‎In this approach‎, ‎one‎ computational method is presented for numerical approximation of variational problems‎. ‎This with variable ‎coeffici‎ents based on Hermite polynomials‎. ‎The properties polynomials the operational matrices derivative and integration are used to reduce optimal control problems solution linear algebraic equations‎. ‎Illustrative examples included demonstrate validity ap...

We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. set notation, and study associated Sobolev spaces order s, denoted by Ws,1(a,b), bounded variation BVs(a,b). Examples, embeddings compactness related to these are addressed, aiming a functional framework suitable for variational models image analysis.