Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in various fields, such as physics,mechanics, chemical technology, population dynamics, biotechnology, and economics (see, e.g., [1–7]). As one of the important topics in the research on differential equations, the boundary value problem has attained a gre...

and Applied Analysis 3 He studied the asymptotic behavior of solutions and found the influence of weight function on the existence of global and blow-up solutions. Wang et al. 10 studied porous medium equation with power form source term ut Δu u, x, t ∈ Ω × 0, ∞ , 1.8 subjected to nonlocal boundary condition 1.2 . By virtue of the method of upper-lower solutions, they obtained global existence,...

asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.from these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. instability condition is obtained and g...

The controllability problem for a class of impulsive fractional-order semilinear control system with nonlocal initial condition has been considered. Sufficient condition for the controllability is established by means of solution operator and application of Banach contraction theorem.

The Cahn--Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. In recent times, various dynamic boundary conditions have been introduced model interactions materials with more precisely. To take long-range into account, we propose a new consisting nonlocal subject condition that also type and contains an additional penalization term. We ...

Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in various fields, such as physics, mechanics, aerodynamics, chemistry, and engineering and biological sciences, involves derivatives of fractional order. Fractional differential equations also provide an excellent tool for the description of memory and he...

We ask the question: is it possible to measure nonlocal properties of a state instantaneously? Relativistic causality restricts how this can be done, but we show here, for the bipartite two dimensional case, that every nonlocal variable of the system can be measured instantaneously. A necessary condition for a general nonlocal measurement on a bipartite system is presented. This essay was writt...

In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus,  it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...

Three parallel algorithms for solving the 3D problem with nonlocal boundary condition are considered. The forward and backward Euler finite-difference schemes, and LOD scheme are typical representatives of three general classes of parallel algorithms used to solve multidimensional parabolic initial-boundary value problems. All algorithms are modified to take into account additional nonlocal bou...

In this work, we study the existence of mild solutions and strict solutions of semilinear functional evolution equations with nonlocal conditions, where the linear part is non-autonomous and generates a linear evolution system. The fraction power theory and α-norm are used to discuss the problems so that the obtained results can be applied to the equations in which the nonlinear terms involve s...