This paper presents a numerical scheme for solving nonlinear time-fractional differential equations in the sense of Caputo. This method relies on the Laplace transform together with the modified Adomian method (LMADM), compared with the Laplace transform combined with the standard Adomian Method (LADM). Furthermore, for the comparison purpose, we applied LMADM and LADM for solving nonlinear time-fractional differential equations to identify the differences and similarities. Finally, we provided two examples regarding the nonlinear time-fractional differential equations, which showed that the convergence of the current scheme results in high accuracy and small frequency to solve this type of equations.

In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

The research deals with a historical study of the materials written by the manuscript since the beginning of its inception in the Arab era in the pre-Islamic era and the origin of Islamic and the following in successive eras.It is a variety of materials ,including Al-Asab,karanif ,parchment ,leather and many other

The research aims to identify the predominant habits and behaviors promoted by American action films frequently streamed on Cinemana website—a specialized platform for streaming films and series as the most followed platform. This platform offers a range of film genres, including the latest releases, free of charge. Using a simple random sampling method, twenty action films were selected for the study. Consequently, the researcher opted for a descriptive-analytical approach, deemed most appropriate for achieving the research objectives, employing content analysis as a tool to scrutinize these films. The findings highlighted that behavioral habits associated with scenes of violence, destruction, sabotage, revenge

The scholars of Arabic - may God reward them with the reward of the doers of good - laid down the rules of this language, the cycle of which never ceases to dazzle minds, so they adopted principles according to which they judged the denomination of this word, and the accusative of that, and determined in its light the worker and the done, until they reached us the rules and foundations of our dear language, and it is obvious that they differ. The origins of grammarians from one school of thought to another, or from one world to another, especially with regard to the subsidiary rules, and this difference was clearly reflected in what we have received from the rules, as we find a difference in the rulings that they restricted to the one fa

This study illustrates the impact of non-thermal plasma (Cold Atmospheric Plasma CAP) on the lipids blood, the study in vivo. The lipids are (cholesterol, HDL-Cholesterol, LDL-Cholesterol and triglyceride) are tested. (FE-DBD) scheme of probe diameter 4cm is used for this purpose, and the output voltage ranged from (0-20) kV with variable frequency (0-30) kHz. The effect of non-thermal atmospheric plasma on lipids were studied with different exposure durations (20,30) sec. As a result, the longer plasma exposure duration decreases more lipids in blood.

The approximate solution of a nonlinear parabolic boundary value problem with variable coefficients (NLPBVPVC) is found by using mixed Galekin finite element method (GFEM) in space variable with Crank Nicolson (C-N) scheme in time variable. The problem is reduced to solve a Galerkin nonlinear algebraic system (NLAS), which is solved by applying the predictor and the corrector method (PCM), which transforms the NLAS into a Galerkin linear algebraic system (LAS). This LAS is solved once using the Cholesky technique (CHT) as it appears in the MATLAB package and once again using the General Cholesky Reduction Order Technique (GCHROT), the GCHROT is employed here at first time to play an important role for saving a massive time. Illustrative

The problem of water scarcity is becoming common in many parts of the world, to overcome part of this problem proper management of water and an efficient irrigation system are needed.  Irrigation with a buried vertical ceramic pipe is known as a very effective in the management of irrigation water.  The two- dimensional transient flow of water from a buried vertical ceramic pipe through homogenous porous media is simulated numerically using the HYDRUS/2D software.  Different values of pipe lengths and hydraulic conductivity were selected.  In addition, different values of initial volumetric soil water content were assumed in this simulation as initial conditions.  Different value