In this paper, we will study and prove the existence and the uniqueness theorems
of solutions of the generalized linear integro-differential equations with unequal
fractional order of differentiation and integration by using Schauder fixed point
theorem. This type of fractional integro-differential equation may be considered as a
generalization to the other types of fractional integro-differential equations
Considered by other researchers, as well as, to the usual integro-differential
equations.

The Digital Elevation Model (DEM) has been known as a quantitative description of the surface of the Earth, which provides essential information about the terrain. DEMs are significant information sources for a number of practical applications that need surface elevation data. The open-source DEM datasets, such as the Advanced Space-borne Thermal Emission and Reflection Radiometer (ASTER), the Shuttle Radar Topography Mission (SRTM), and the Advanced Land Observing Satellite (ALOS) usually have approximately low accuracy and coarser resolution. The errors in many datasets of DEMs have already been generally examined for their importance, where their quality could be affected within different aspects, including the types of sensors, algor

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

In this work, Elzaki transform (ET) introduced by Tarig Elzaki is applied to solve linear Volterra fractional integro-differential equations (LVFIDE). The fractional derivative is considered in the Riemman-Liouville sense. The procedure is based on the application of (ET) to (LVFIDE) and using properties of (ET) and its inverse. Finally, some examples are solved to show that this is computationally efficient and accurate.

     The accurate 3-D coordinate's measurements of the global positioning systems are essential in many fields and applications.  The GPS has numerous applications such as: Frequency Counters, Geographic Information Systems, Intelligent Vehicle Highway Systems, Car Navigation Systems, Emergency Systems, Aviations, Astronomical Pointing Control, and Atmospheric Sounding using GPS signals, tracking of wild animals, GPS Aid for the Blind, Recorded Position Information, Airborne Gravimetry and other uses. In this paper, the RTK DGPS mode has been used to create precise 3-D coordinates values for four rover stations in Baghdad university camp. The HiPer-II Receiver of global positioning system was used to navigate the

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

In this paper, we consider inequalities in which the function is an element of n-th partially order space. Local and Global uniqueness theorem of solutions of the n-the order Partial differential equation Obtained which are applications of Gronwall's inequalities.

A new modified differential evolution algorithm DE-BEA, is proposed to improve the reliability of the standard DE/current-to-rand/1/bin by implementing a new mutation scheme inspired by the bacterial evolutionary algorithm (BEA). The crossover and the selection schemes of the DE method are also modified to fit the new DE-BEA mechanism. The new scheme diversifies the population by applying to all the individuals a segment based scheme that generates multiple copies (clones) from each individual one-by-one and applies the BEA segment-wise mechanism. These new steps are embedded in the DE/current-to-rand/bin scheme. The performance of the new algorithm has been compared with several DE variants over eighteen benchmark functions including sever

The nonhomogeneous higher order linear complex differential equation (HOLCDE) with meromorphic (or entire) functions is considered in this paper. The results are obtained by putting some conditions on the coefficients to prove that the hyper order of any nonzero solution of this equation equals the order of one of its coefficients in case the coefficients are meromorphic functions. In this case, the conditions were put are that the lower order of one of the coefficients dominates the maximum of the convergence exponent of the zeros sequence of it, the lower order of both of the other coefficients and the nonhomogeneous part and that the solution has infinite order. Whiles in case the coefficients are entire functions, any nonzero solutio