The synchronization problem for impulsive fractional-order Cohen–Grossberg neural networks with generalized proportional Caputo fractional derivatives changeable lower limit at any point of impulse is studied. We consider the cases when control input acting continuously as well it instantaneously times. defined global Mittag–Leffler a generalization exponential synchronization. obtained some su...

In this study, the meshless collocation approach is used to determine numerical solution generalized time-fractional Gardner equation. The Crank-Nicolson technique approximate space derivatives, whereas Caputo derivative of fractional order first time derivative. solutions, which show method?s efficacy and accuracy, are pro?vided discussed. shows that our method effective in producing extremely...

in this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. these problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive banach space. to make the nonlinear methods work, some careful analysis of t...

in this paper we apply hybrid functions of general block-pulse‎ ‎functions and legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (fdes)‎. ‎our approach is based on incorporating operational matrices of‎ ‎fdes with hybrid functions that reduces the fdes problems to‎ ‎the solution of algebraic systems‎. ‎error estimate that verifies a‎ ‎converge...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

A fractional model of the Hopfield neural network is considered in case application generalized proportional Caputo derivative. The stability analysis this used to show reliability processed information. An equilibrium defined, which generally not a constant (different than ordinary derivatives and Caputo-type derivatives). We define exponential Mittag–Leffler equilibrium. For this, we extend s...

In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate generalized Caputo fractional derivative (GCFD). Convergence order for (4−α), where α(0<α<1) of GCFD. The local truncation error also provided. Then, we adopt developed establish difference solution advection–diffusion equation with Dirichlet boundary conditions. Furthe...

In this paper, we give new Simpson’s type integral inequalities for the class of functions whose derivatives absolute values are s-convex via generalized proportional fractional integrals. Some results in literature particular cases our results.

The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann–Liouville fractional derivatives. All point groups and the corresponding optimal subgroups are determined. Then, similarity reduction performed given equation some explicit solutions derived. asymptotic behaviours for also discussed. Through concept nonlinear self-adjointness...

The use of non-local operators, defining Riemann–Liouville or Caputo derivatives, is a very useful tool to study problems involving non-conventional diffusion problems. case electric circuits, ruled by non-integer derivatives capacitors with fractional dielectric permittivity, fairly natural frame relevant applications. We techniques, generalized exponential obtain suitable solutions for this t...