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

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.

Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems in

       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.

      In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).

      In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

    The current research focused on the detection of Salmonella typhi and its relationship with the formation of gallstone and gall bladder cancer. Samples were collected from patients aged between 32-67 years (males and females) in Mosul city hospitals. The samples included 30gallbladder fresh tissues from patients suffering from gallstone and 20 formalinfixed-paraffin embedded (FFPE) gallbladder tissue from patients confirmed with gallbladder cancer. The results showed that 33% S. typhi isolates were diagnosed from the tissue samples using conventional methods, biochemical tests and Vitek2. All fresh tissues samples gave positive PCR results for the presence of FliC-d and CdtB genes and 46% positi

Background: obesity is nowadays a pandemic condition. Obese subjects are commonly characterized by musculoskeletal disorders and particularly by non-specific low back pain (LBP). However, the relationship between obesity and LBP remain to date unsupported by an objective measurement of the mechanical behavior of spine and it is morphology in obese subjects. . Objectives: To identify the relationship between obesity and LBP regarding (height, weight, sleeping, chronic diseases, smoking, and steroid). Method: A cross-sectional study was conducted from the first of January 2016 to January 2018 in obe

The gravity field of southern Iraq shows steep gradient of regional trend. The gravity contours over the anticline structures in this area do not show the closure characteristic of these structures. The effect of lateral density variation for Hormuz Salt complicates the case in the area. Higher derivatives are one of the means that have been used to remove the effect of such regional gravity variations, which can easily mask significant structures. Biharmonic Operator is used to delineate these distort structures, follow their extent and at the same time distinguish new features. The Biharmonic operator manipulation has ability to suppress the effect of regional and enhance the local anomalies. The problem with higher derivatives operati