Our aim in this work is to study the classical continuous boundary control vector  problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector,  by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations

This study focused on the improvement of the quality of gasoline and enhancing its octane number by the reduction of n-paraffins using zeolite 5A. This study was made using batch and continuous mode. The parameters which affected the n-paraffin removal efficiency for each mode were studied. Temperature (30 and 40 ˚C) and mixing time up to 120 min for different amounts of zeolite ranging (10-60 g) were investigated in a batch mode. A maximum removal efficiency of 64% was obtained using 60 g of zeolite at 30 ˚C after a mixing time 120 min. The effect of feed flow rate (0.3-0.8 l/hr) and bed height (10-20 cm) were also studied in a continuous mode. The equilibrium isotherm study was made using different amounts of zeolite (2-20 g) and the

This research is addressing the effect of different ferrocene concentration (0.00, 2.15x10-3, 4.30x10-3, 8.60x10-3, and 12.9x10-3) on the bulk free radical polymerization of methyl methacrylate monomer in benzene using benzoyl peroxide as initiator. The polymerization was conducted at 60º C under free oxygen atmosphere. The resulting polymers were characterized by FTIR. The results were compared with the presence and absence of ferrocene at 10% conversion. The %conversion was 3.04% with no ferrocene present in the polymerization medium and its increase to 9.06 with a first lowest ferrocene concentration added, i.e. 2.15 x10-3mol/l. This was positively reflected on the poly(methyl methacrylate) molecular weight measured by viscosity techniq

     In this study, an efficient novel technique is presented to obtain a more accurate analytical solution to nonlinear pantograph differential equations. This technique combines the Adomian decomposition method (ADM) with the homotopy analysis method concepts (HAM). The whole integral part of HAM is used instead of an integral part of ADM approach to get higher accurate results. The main advantage of this technique is that it  gives a large and more extended convergent region of iterative approximate solutions for long time intervals that rapidly converge to the exact solution. Another advantage is capable of providing a continuous representation of the approximate solutions, which gives  better information over whole time interv

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

      In this paper, several types of space-time fractional partial differential equations has been solved by using most of special double linear integral transform ”double  Sumudu ”. Also, we are going to argue the truth of these solutions by another analytically method “invariant subspace method”. All results are illustrative numerically and graphically.

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

       In this work, we prove that the triple linear partial differential equations (PDEs) of elliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr) has a unique "state" solution vector (SSV)  by utilizing the Galerkin's method (GME). Also, we prove the existence of a classical continuous boundary optimal control vector (CCBOCVr) ruled by the TLEPDEs. We study the existence solution for the triple adjoint equations (TAJEs) related with the triple state equations (TSEs). The Fréchet derivative (FDe) for the objective function is derived. At the end we prove the necessary "conditions" theorem (NCTh) for optimality for the problem.