17 research outputs found
On Comparison Study between Double Sumudu and Elzaki Linear Transforms Method for Solving Fractional Partial Differential Equations
في هذا البحث، استخدمنا طريقتي التحويلان التكامليان المضاعفان سمودو و الزاكي للحصول على الحلول العددية لبعض انواع المعادلات التفاضلية الجزئية الكسرية ذات المعاملات الثابتة، ووضحنا كفاءة الطريقة بتقديم بعض الامثلة العددية المحسوبة باستخدام برنامجي ماثكاد 15 و ماتلاب R2015a In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using Mathcad 15.and graphic in Matlab R2015a
Numerical and analytic method for solvingproposal New Type for fuzzy nonlinear volterra integral equation
In this paper, we proved the existence and uniqueness and convergence of the solution of new type for nonlinear fuzzy volterra integral equation . The homotopy analysis method are proposed to solve the new type fuzzy nonlinear Volterra integral equation . We convert a fuzzy volterra integral equation for new type of kernel for integral equation, to a system of crisp function nonlinear volterra integral equation . We use the homotopy analysis method to find the approximate solution of the system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy volterra integral equation . Some numerical examples is given and results reveal that homotopy analysis method is very effective and compared with the exact solution and calculate the absolute error between the exact and AHM .Finally using the MAPLE program to solve our problem
Solvability of Some Types for Multi-fractional Integro-Partial Differential Equation
خلال البحث تم المناقشة وبالتفصيل قابلية الحل لبعض الأنظمة من المعادلات المتعددة التفاضلية التكاملية ذات الرتب الكسرية باستخدام مفهوم مسائل كوشي المختصرة وايضا نظرية شبه زمرة المختارة مع بعض الشروط الضرورية والكافية.In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions.
Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations
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 Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives
The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions
Stability of nonlinear impulsive higher order differential – fractional integral delay equations with nonlocal initial conditions
The aim of this paper is to investigate some types of stability such as generalized Hyers-Ulam- Rassias stability(G-H-U-R-stabile) and the relation with Hyers-Ulam(H-U-stabile) stable and Hyers-Ulam-Rassias stable (H-U-R-stabile) and generalized Hyers-Ulam stable (G-H-U- stable) to obtain which one guarantee to satisfy stability of equations included a nonlinear function some of them contains a delay time of solution and the other contain a vector of different order of derivatives for the solution to n-time and vector of fractional order of integrals with different fractional orders and that was the for using a claculse of fractional calculus to satisfies the issue of this techniques. Moreover, the nonlocal initial values for the proposal equation of nonlinear impulsive higher order differential – fractional integral delay time equations which are adding more interesting for nonlinear analytic object of nonlinear higher order integro – fractional order impulsive classes, and the impulsive difference of the equation has some necessary conditions to prove the results of solution to be stable with certain type has related with other types. The necessary and sufficient conditions which assumed on this nonlinear higher order integro-differential impulsive equation have been achieved the stability with interesting certain estimates obtain through the proving technique. Also the uniqueness of solution has been studied with same conditions was presented for stability and used for that issue a contraction fixed point theorem
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Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021
BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation
Holder's Inequality ρ–Mean Continuity for Existence and Uniqueness Solution of Fractional Multi-Integrodifferential Delay System
We herein present the detailed results for the existence and uniqueness of mild solution for multifractional order impulsive integrodifferential control equations with a nonlocal condition involving several types of semigroups of bounded linear operators, which were established on probability density functions related with the fractional differential equation. Additionally, we present the necessary and sufficient conditions to investigate Schauder’s fixed point theorem with Holder’s inequality ρ–mean continuity and infinite delay parameter to guarantee the uniqueness of a fixed point
Solution of Some Types for Composition Fractional Order Differential Equations Corresponding to Optimal Control Problems
The approximate solution for solving a class of composition fractional order optimal control problems (FOCPs) is suggested and studied in detail. However, the properties of Caputo and Riemann-Liouville derivatives are also given with complete details on Chebyshev approximation function to approximate the solution of fractional differential equation with different approach. Also, the relation between Caputo and Riemann-Liouville of fractional derivative took a big role for simplifying the fractional differential equation that represents the constraints of optimal control problems. The approximate solutions are defined on interval [0,1] and are compared with the exact solution of order one which is an important condition to support the working method. Finally, illustrative examples are included to confirm the efficiency and accuracy of the proposed method
SOME NEW RELATIONSHIPS BETWEEN THE FRACTIONAL DERIVATIVES OF FIRST, SECOND, THIRD AND FOURTH CHEBYSHEV WAVELETS
Soil acidity and salinity are major constraints for agricultural productivity around the world. Improving beneficial plant-microbe interactions in the rhizosphere and endosphere could improve plant tolerance to acidity and salinity and increase crop yield and productivity. However, soil acidity and salinity can adversely impact symbiotic interactions of plants with arbuscular mycorrhizal fungi (AMF) and nitrogen-fixing bacteria (NFB), which play an important role in plant nutrition. Soil amendments or foliar application of signaling compounds were shown to modulate microbial diversity and composition in the rhizosphere and plant endosphere and could be potential management tools to improve beneficial plant-microbial interactions in acidic and saline soils. However, it is not clear how native microbial community in the rhizosphere and endosphere of a legume crop respond to acidity and salinity stress and soil amendments. It is also not clear whether exogenous application of signaling compounds can significantly modulate rhizosphere and endosphere microbiome structure of a legume crop. Particularly, AMF and NFB responses to soil amendments and signaling compounds needs to be investigated in acidic and saline soils. To address these knowledge gaps, two studies were conducted to evaluate soil and foliar amendments to improve plant-microbe interactions in a legume crop (cowpeas, Vigna unguiculata (L.) Walp.) grown in an acidic and a saline soil. A comprehensive assessment of plant growth and development and microbiome composition in the rhizosphere and endosphere including legume-rhizobia and plant root-AMF symbiosis were evaluated in both studies.
In the first experiment, biochar as a soil amendment and salicylic acid (SA) as a foliar applied stimulant were evaluated for their impacts on soil pH, nutrient uptake, nodulation, AMF colonization, diversity and composition of rhizosphere and endophytic microbiome of cowpea plants grown in acidic soils (pH = 4.8). Results showed that soil acidity reduced nodulation, plant nutrient concentrations, diversity of rhizosphere microbes and pod yield. Biochar (BC) amendment was more effective in improving plant nutrient uptake and pod yields than SA treatment. Soil pH was increased to around 5.8 ± 0.2 in the BC treatment compared to control (5.0 ± 0.2). Similarly, nodulation numbers were higher in BC treatment, which resulted in higher N concentrations in the leaves compared to SA treatment. Percent AMF colonization was also increased significantly in BC treatment, which recorded higher leaf P concentrations. Treatment of SA significantly improved AMF colonization and abundance of AMF taxa in the rhizosphere, however, plant nutrient concentrations and pod yield did not significantly differ from unamended control. Both BC and SA significantly altered the microbial composition in the rhizosphere and plant endosphere. Treatment of BC also significantly increased the relative abundance of several plant beneficial taxa such as Bacillus, Pseudomonas, Penicillium, Rhizobium and Bradyrhizobium compared to control. Based on the results of this study it was concluded that BC application to an acidic soil was effective in improving plant-microbe interactions and pod yields of cowpea plants grown in an acidic soil.
A second greenhouse study was conducted to evaluate compost (CMP) and gypsum (GYP) as soil amendments and foliar application of strigolactones (SL), salicylic acid (SA) and coumarins (COU) for their impacts on plant-microbe interactions of cowpea grown in a saline soil (pH = 8.5). Crop growth and development, diversity and composition of rhizosphere and endophytic microbiome, arbuscular mycorrhizal fungi (AMF) colonization, nodulation, plant nutrient concentrations were estimated from the treatments. Results showed that soil salinity adversely impacted plant nutrient uptake, AMF colonization and pod yields. Among the amendment treatments, SL+SA treatment produced the highest cowpea pod yield followed by CMP amendment. Highest nodulation and root colonization were noted in SL+SA treated plants. Significantly higher relative abundance of several plant beneficial microbes including a Streptomyces species and several AMF (Rhizophagus and Diversispora) were noted in the rhizosphere and roots of SL+SA treated plants compared to control. Based on the results of this study, it was concluded that foliar application of SL+ SA was most effective in improving plant-microbe interactions and pod yield of cowpea plant grown in a saline soil.
It was demonstrated by these two studies that several beneficial microbes in the rhizosphere and endosphere of a legume crop were sensitive to acidity and salinity stress. It was also clear that various soil amendments and exogenous application of signaling compounds significantly altered rhizosphere and endosphere microbiome structure of a legume crop, and improved cowpea interactions with AMF and NFB. Using effective soil amendments such as biochar in acidic soil and foliar application of SL and SA for plants grown in saline soils are potential agriculture management avenues for improving soil health and productivity in acidic and saline soils