Abstract We consider an optimal control problem containing a system described by partial nonlinear differential equation with the fractional Dirichlet–Laplacian, associated to integral cost. investigate existence of solutions for such problem. In our study we use Filippov’s approach combined lower closure theorem orientor fields.

Partial differential equations (PDEs) are concise and understandable representations of domain knowledge, which essential for deepening our understanding physical processes predicting future responses. However, the PDEs many real-world problems uncertain, calls PDE discovery. We propose symbolic genetic algorithm (SGA-PDE) to discover open-form directly from data without prior knowledge about e...

<p style='text-indent:20px;'>In this paper, we study the numerical approximation of a system PDEs which arises from an optimal control problem for time-fractional Fokker-Planck equation with time-dependent drift. The is composed backward Hamilton-Jacobi-Bellman and forward equation. We approximate Caputo derivatives in by means L1 schemes Hamiltonian finite differences. scheme constructed...

In this article, we present an efficient local meshless method for the numerical treatment of 3-D convection-diffusion PDE. The demand techniques increment because its nature and simplicity usage in higher dimensions. This technique approximates solution on set uniform scattered nodes. space derivatives models are discretized by proposed procedure though time fractional part is Liouville-Caputo...

in this paper, we develop an efficient legendre wavelets collocation method for well known time-fractional heat equation. inthe proposed method, we apply operational matrix of fractionalintegration to obtain numerical solution of the inhomogeneoustime-fractional heat equation with lateral heat loss and dirichletboundary conditions. the power of this manageable method isconfirmed. moreover, the ...

This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To ill...

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

Normal rat pregnancy is characterized by plasma volume expansion due to renal sodium retention and is associated with a blunted response to natriuretic stimuli, such as atrial natriuretic peptide (ANP). ANP signals via cGMP, and phosphodiesterases (PDE) inactivate cGMP and terminate the natriuretic response. We previously reported that increased medullary PDE-5 activity occurs in rat pregnancy,...

n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.