In this study, we present the new generalized derivative and integral operators which are based on the newly constructed new generalized Caputo fractal–fractional derivatives (NGCFFDs). Based on these operators, a numerical method is developed to solve the fractal–fractional differential equations (FFDEs). We approximate the solution of the FFDEs as basis vectors of shifted Legendre polynomials (SLPs). We also extend the derivative operational matrix of SLPs to the generalized derivative operational matrix in the sense of NGCFFDs. The efficiency of the developed numerical method is tested by taking various test examples. We also compare the results of our proposed method with the methods existed in the literature In this paper, we specified the fractal–fractional differential operator of new generalized Caputo in three categories: (i) different values in  and fractal parameters, (ii) different values in fractional parameter while fractal and  parameters are fixed, and (iii) different values in fractal parameter controlling fractional and  parameters.

Lithostratigraphically, the Sidi As sid Formation (Upper Cretaceous) in the El Zintan section (JabalNafusah, NW Libya) consists of three units: upper marl, middle marl with intercalations of dolostone, and lower dolostone. Based on crystal size and shape, three types of dolomite have been classified. Fine crystalline dolomite (D1) consists of nonplanar dolomites, fine to medium crystalline dolomite (D2), and very coarse, consisting of mostly planar dolomites (D-3). The Cathodoluminescence technique also showed that most of these dolomites have bright yellow to red and dull orange luminescence and zoning. Based on X-ray diffraction (XRD), all dolomites are relatively well ordered and non to nearly stoichiometric dolomite. The stable isotopic studies and element analysis show that the major elements such as sodium (D1: 412.166 ppm; D2: 175 ppm; D3: 420 ppm), strontium (D1: 107 ppm; D2: 85 ppm; D3: 81.2 ppm), manganese (D1: 271 ppm; D2: 91 ppm; V3: 242 ppm), and iron (D1: 4856.66 ppm; D2: 373 ppm; D3: 3287 ppm) and the values of the stable isotope of oxygen (D1:-2.202‰; D2:-2.131; D3:-4.359‰) and carbon (D1: 2.080; D2: 2.076‰; D3: 1.581‰). The values of major elements and depletion of the carbon and oxygen isotopes can be related to the effects of temperature diagenetic, and mesosaline reflux of dolomitizing fluids during the early diagenesis. These dolomites originated in a tidal environment in this Formation. The major sources of magnesium for the dolomites are seawater and hypersaline fluids.

The study of integral equations is one of the most important topics that researchers are interested in, it arises in many scientific fields for instance engineering, and mathematical and scientific analysis. The first who mentioned the term integral equations is Du Bois-Reymond (1888). As a result, a lot of interest appeared from researchers, and the most important of these researchers are Laplace, Fourier, Poission, Liouville, and Able. Upadhyay et al., (2015) provided some special types of integral equations. The quadratic integral equation is a special form of integral equations. The initial study appeared by Chandrasekhar (1947). More appearance of Quadratic integral equation was in the theory of radiative transfer, kinetic theory of gases, in the theory of neutron transport, and in the traffic theory, see Argyros (1985), Banaś et al. (2007), El-Sayed et al. (2008).

Water used for crop irrigation is often of insufficient quality in the Mediterranean region, where sea water invades the porous karst matrix and salinizes Sources of soil and water. Measuring the productivity of horticultural crops under saline conditions helps decide if and when crops should be irrigated if water is saline, thus balancing crop water and salt stress. To examine the effects of saline irrigation water on (Vicia faba L.) biomass and yield parameters, a greenhouse pot experiment was set up.NaCl salinity was applied as follows: After 15 days from irrigation, plants were subjected to graded levels of salinity: 0, 50, 100, 200 and 300 mM NaCl, applied in stepwise daily increments to avoid induction of salt shock to the seedlings. Height of Plant (cm), The number of lateral branches , number of( leaves, pods, seeds) per plant, shoot weight (g), is correlated with an increase in stressed plant photosynthetic pigments. five weeks after salinity therapy, the weight of the pod (g) and the weight of the seed (g) were determined. Increased irrigation water salinity statistically significantly decreased the calculated parameters (P<0.05) relative to regulation , except for the number of branches and pods. Salinity is associated with an increase in photosynthetic pigments in stressed plants. The productivity of Vicia faba has decreased in proportion to the degree of salinity of irrigation water

Exact string-matching algorithms have become very supreme in many bioinformatics tools. Despite the abundance and diversity of such algorithms, exposing them to real-time experimental analysis has been critical. This study was conducted to evaluate the efficiency of ten exact-string matching algorithms on large-scale genomic sequences from a runtime perspective. To define the most efficient algorithms are qualified to handle the short alphabet used for nucleic acid coding. The methodology promoted for this study was the factorial experiment with Randomized Complete Block Design (FRCBD). Under influence of four independent parameters, four levels of pattern lengths, four levels of pattern indices, two levels of programming languages, and ten levels of algorithmic architecture. The yield of the tested algorithms was calculated in nanoseconds. One-way ANOVA and Two-way ANOVA tests with post-hoc Games-Howell test were used separately for statistical analysis. In this study two widely accepted programming languages, C# and JAVA were used to speculate the possible effect of programing language on algorithm performance. The One-way ANOVA results revealed that the Backward-Oracle-Matching (BOM), Zhu-Takaoka (ZT), and Horspool's (HP) algorithms exhibited the highest final performance correspondingly. These algorithms have demonstrated an efficiency of up to 250% higher than other algorithms. The results of two-way ANOVA revealed a significant interaction between programing language adopted and execution time with the absence of pattern lengths and pattern index effect. The combination of the C# programing language and the Backward-Oracle-Matching algorithm produced the most effective performance on genomic sequences. 

Short Tandem Repeats (STRs) are one of the utmost mutable provinces in the human genome. They comprise tandem repeating DNA sequences ranging in length from two to six base pairs. Owing to their significant mutation rate, they exhibit considerable variation in pattern among populations and the capacity to be passed on from generation to generation. These loci are broadly employed in medicine, biology, and criminal investigation. They are pivotal in the genesis of a variety of genetic illnesses and have been intensively investigated in forensics, population genetics, and genetic genealogy. Although many implementations that manage STR loci are offered, the overwhelming majority of them rely primarily on the Command-Line Interface (CLI) inputs, which frequently necessitate the implementation of tools carried out in various scripting languages. Installing and launching programs through the Command Line (CL) is timeconsuming and/or unprofitable for many students and scholars. The fundamental intention of this project is to develop a cross-platform Graphical User Interface (GUI) package directed to the Combined DNA Index System (CODIS) STR analysis. Zenobia is a Java-based application considered as a step in consistently making CL-only programs available to more apprentices and researchers. In general, Zenobia's application outcomes satisfy the evaluation metrics for efficiency and time consumption. However, more genetic markers should be introduced to increase productivity of the application.