In this work we introduce and perform a study on the multitime multi-objective fractional variational problem of minimizing a vector of quotients of path independent curvilinear integral functionals (MFP ) subject to certain partial differential equations (PDE) and/or partial differential inequations (PDI), using a geometrical language. The paper is organized as follows: §1 formulates a PDI&PDE...

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...

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,...