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.
Research Summary:
Seeking happiness and searching for it have been among the priorities of mankind from the beginning of his creation and will remain so until the end of this world, and even in the next life, he seeks happiness, but the difference is that a person can work in this world to obtain it, but in the next life he is expected to get what he done in this world. And among these reasons are practical actions that a person undertakes while he intends to draw close to God Almighty, so they lead him to attain his desired perfection, and to attain his goals and objectives, which is the minimum happiness in this life, and ultimate happiness after the soul separates the body, and on the day of the judgment, Amon
... Show MoreThe aim of the current study was to develop a nanostructured double-layer for hydrophobic molecules delivery system. The developed double-layer consisted of polyethylene glycol-based polymeric (PEG) followed by gelatin sub coating of the core hydrophobic molecules containing sodium citrate. The polymeric composition ratio of PEG and the amount of the sub coating gelatin were optimized using the two-level fractional method. The nanoparticles were characterized using AFM and FT-IR techniques. The size of these nano capsules was in the range of 39-76 nm depending on drug loading concentration. The drug was effectively loaded into PEG-Gelatin nanoparticles (≈47%). The hydrophobic molecules-release characteristics in terms of controlled-releas
... Show MoreWaste is one of the most important problems affecting the city’s environment and its urban landscape, which results from the activities and activities of man and the natural environment. Its sources have varied between residential, commercial, industrial, medical and hazardous, and its spread in cities, on roads and on abandoned open lands, has led to significant negative effects and risks to human health and the environment.
Therefore, there were serious attempts to deal with waste and follow sequential steps that formed a waste management system such as (collection, sorting, transport, then treatment and disposal). Preventing and reducing waste, then recycling and recovering by composting or burning, and ending with bu
... Show MoreCorruption, in all its categories and forms, is regarded as the nowadays virus which has greatly spread in most institutes and society, a matter that cause a great waste of resources.
According to the reports of international transparency Institute, Iraq is regarded as one of the greatest countries in corruption.
Regardless of the reasons and forms of corruption, the retreat in work – values and ethics are the main reasons behind that.
Being the main source of providing qualified staff "educators" for the working market, the high education institutes face great challenges in standing against corruption inside and outside
... Show MoreFor Spanish learners who are not immersed in everyday contexts, such as students of Spanish as a foreign language, interaction with native speakers is an enriching experience that allows them to contrast their knowledge in a meaningful way. For its part, understanding the cognitive and grammatical functions of the so-called verbs of change plays an essential role in the development of everyday conversation,including the management of aspects such as dialectal variations.In relation to this important function, the central theme of our proposal is verbs of change. The latter have been the research base of several linguists who highlight, amidst their complex functioning in Spanish, positive communicative bases. By observing these perspecti
... Show MoreThe current study aims to examine the level of problems faced by university students in distance learning, in addition to identify the differences in these problems in terms of the availability of internet services, gender, college, GPA, interactions, academic cohort, and family economic status. The study sample consisted of (3172) students (57.3% females). The researchers developed a questionnaire with (32) items to measure distance learning problems in four areas: Psychological (9 items), academic (10 items), technological (7 items), and study environment (6 items). The responses are scored on a (5) point Likert Scale ranging from 1 (strongly disagree) to 5 (strongly agree). Means, standard deviations, and Multivariate Analysis of Vari
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