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 main focus of this research is to examine the Travelling Salesman Problem (TSP) and the methods used to solve this problem where this problem is considered as one of the combinatorial optimization problems which met wide publicity and attention from the researches for to it's simple formulation and important applications and engagement to the rest of combinatorial problems , which is based on finding the optimal path through known number of cities where the salesman visits each city only once before returning to the city of departure n this research , the benefits  of( FMOLP)   algorithm is employed as one of the best methods to solve the (TSP) problem and the application of the algorithm in conjun

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an

Background: Management of immature permanent teeth with necrotic pulp is considered challenging to the clinician. Regeneration of pulp tissue is a relatively new approach for management of these teeth that allow continuation of root maturation rather than formation of just a calcific barrier as in apexification. Method: 9 years-old girl with traumatized upper left central incisor. The clinical and radiographical examinations revealed uncomplicated crown fracture, tenderness to percussion, absence of response to cold vitality test. Diagnostic X-ray revealed open apex with periapical radiolucency. Revascularization was suggested to treat the tooth, starting with irrigation of canal with 5% NaOCl + 3% H2O2, followed by 2 weeks of triple antibi

This work is an experimental investigation for single basin-single slope solar still coupled with an evacuated tube solar collector. The work is carried out under the climatic conditions of Baghdad city (33.2456º North and East latitude, 44.3337º longitude) through certain days of the months of the year 2019 to study the impact of using evacuated tube solar collector on the daily productivity and efficiency under the outdoors climatic conditions. It was found that using the evacuated tube solar collector increase daily productivity from 2.175 kg/  to 2.95 kg/ for 9 hours (35.63 %) for clear days, also an enhancement about 10.97 % in daily efficiency.

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 .

    New class A^* (a,c,k,β,α,γ,μ)  is introduced of meromorphic univalent functions with positive coefficient f(z)=â–¡(1/z)+∑_(n=1)^∞▒〖a_n z^n 〗,(a_n≥0,z∈U^*,∀ n∈ N={1,2,3,…}) defined by the integral operator in the punctured unit disc U^*={z∈C∶0<|z|<1}, satisfying |(z^2 (I^k (L^* (a,c)f(z)))^''+2z(I^k (L^* (a,c)f(z)))^')/(βz(I^k (L^* (a,c)f(z)))^''-α(1+γ)z(I^k (L^* (a,c)f(z)))^' )|<μ,(0<μ≤1,0≤α,γ<1,0<β≤1/2 ,k=1,2,3,… ) . Several properties were studied like coefficient estimates, convex set and weighted mean.

This study presents experimental and numerical investigations on seven one-way, reinforced concrete (RC) slabs with a new technique of slab weight reduction using polystyrene-embedded arched blocks (PEABs). All slabs had the same dimensions, steel reinforcement, and concrete compressive strength. One of these slabs was a solid slab, which was taken as a control slab, while the other six slabs were cast with PEABs. The main variables were the ratio of the length of the PEABs to the length of the slab (lp/L) and the ratio of the height of the PEABs to the total slab depth (hP/H). The minimum decrease in the ultimate load capacity was about 6% with a minimum reduction in the slab weight of 15%. In contrast, the maximum decrease in the

In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

     This paper is devoted to compare the performance of non-Bayesian estimators represented by the Maximum likelihood estimator of the scale parameter and reliability function of inverse Rayleigh distribution with Bayesian estimators obtained under two types of loss function specifically; the linear, exponential (LINEX) loss function and Entropy loss function, taking into consideration the informative and non-informative priors. The  performance of such estimators assessed on the basis of mean square error (MSE) criterion. The Monte Carlo simulation experiments are conducted in order to obtain the required results.