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.

In The Name of Allah Most Gracious Most Merciful

Scholars, past and present, have paid attention to the books of Fasting and Hajj, and they have compiled literature on that, and they have written treatises and researches. The best days, and as for the pilgrimage, it is one of the great pillars of Islam, which God Almighty has distinguished by making its rituals in the best of places, which is the Sacred House of God.

Modern digital technologies have affected the means of communication in terms of structure, function and methods of dealing with them, and the communication process has changed, becoming bilateral, reciprocal and interactive, after it was one-way and limited in circulation and the roles changed, so the receiver became the sender and reversed is correct, and the culture of the active user and the participant spread, and the communication process became continuous.
The international information network has provided new electronic channels in the media and communication that are not known and opened a new era for these means, which led to a trend towards digital media in an unprecedented way.
The new communication platforms are the re

That interdependence in Islam is cooperation, love and fraternity and give and take
and let him look rich to the poor, every Muslim is himself liable hungry and poor no matter
how many races and colors. That interdependence is cruel, spending for God and is the
greatest supporter of charities that deal with housing, food and medicine for the unemployed
and needy, and social solidarity the consolidation of the values of brotherhood and love,
where is the greatest support of corrupt and concerted community and causes prosperity in
societies and has a significant impact on the unity of Muslims and their club and their
collection. The Islamic regime tops major systems in entrusting the achievement claimed the
lives of

Research summary

Praise be to God, and prayers and peace be upon our master Muhammad, his family and companions until the Day of Judgment.

As for after:

It is the right of every nation to take care of its scientific heritage, and to reveal its human civilizational impact, and the Arabs are the richest nations in heritage, as they had in every period of time a sign and pride, the Arabs fulfilled their duty towards humanity, and they carried out a large part of their scientific activity towards humanity.

Therefore, highlighting some of the scientific aspects of the civilized activity of the Arabs, and removing some of the illusions spread by some malicious people, is a human duty before it is a national duty.

The need for an intellectual understanding of the context from many aspects' dictates understanding the ways through which the graphic designer walks in simulating the intent of the design process and elevating it to levels of communicative perception that leads to communicating the idea to the recipient, and it is thus a need closely related to the context, if it is historical. Culturally or socially, and between the mechanisms of selecting and operating the elements and units of the graphic and design achievement. On this basis, the role of context in graphic design can be studied.

The research included four chapters, the first chapter of the research problem and the need for it, and the aim of the research was (discovering the

In the last few years, following the relative stability of the political, economic, and security environments, Iraq has embarked on a transformation towards an ambitious program of automation across various sectors. However, this automation program faces numerous challenges, including significant investments in technology and training, addressing social impacts, and combating widespread illiteracy