الأصول الجامعة بين كبرى الفرق الإسلامية

The Muslim nation shows great diversity in many ways: Ethnical, lingual, tribal, racial, colour, cultural, etc. Nevertheless, such differences have never been supposed to impede their way to their unity. The Muslim nation has far more reasons and mutual foundations to be united. But unfortunately, the Muslim history witnesses squabbles and skirmishes between different sects of this otherwise one Ummah. These disputes led us to the recesses of ignorance and intolerance, which in turn left us lagging behind the world and advancement, and now, we are called the third world, which is not an honour any way. We need to work on the similarities between different sects of the Muslim nation and let them learn how to live together keeping their differences. So that they may get united. All the Muslims sects fundamentally believe in the same set of beliefs, practices, and rituals. The differences in these areas are the differences of diversity and extensions, not of contradiction. This diversity is the beauty of deliberation and discussion, hence a reason for knowledge to grow, it should not be a matter of contentions. We need to highlight the mutual common grounds of Islamic beliefs and religiosity among the sects to unite this nation. We need to teach how to tolerate and respect each other with difference of opinions. We should encourage constructive dialogues between the Muslims sects and let them understand point of views of each other and thus remove the misconception about; each other. We should curb the contentious and discordant voices and build up an atmosphere where a healthy, tolerant and heterogeneous society may emerge and pave the way to Muslim unity and thence to success in this life and the life to come after death. In this perspective, the author of his present study explores to find the teachings and guidance of Islam. This is the theme of the present study.

Fuzzy Fractional Differential Equations

The concept of fuzzy fractional differential equation (FFDE) was introduced by Agar- wal, Lakshmikantham and Nieto [1]. We develop this concept of fuzzy fractional dif- ferential equation and obtain some results about existence and uniqueness of solution of FFDE. In the second chapter we recall some basic knowledge of fuzzy calculus and frac- tional calculus. In third chapter we introduce the concept of Riemann-Liouville integral and Riemann-Liouville derivative for fuzzy functions. Fuzzy derivative is consider in the Seikkala sense. Moreover we give the new results about the properties of fuzzy frac- tional integral and fuzzy fractional derivative. Further, we study the existence and uniqueness of the solution for a class of fractional differential equation with fuzzy ini- tial value. The fractional derivatives are considered in the Riemann-Liouville sense. In fourth chapter we establish that fuzzy fractional differential equation is equiv- alent to the fuzzy integral equation and using this equivalence we prove the existence and uniqueness of solution of fuzzy fractional differential equation. Fuzzy derivative is considered in the Goetschel-Voxman sense. Also the applications of the existence and uniqueness theorem has been given. In fifth chapter we present results regarding the existence of the solutions of fuzzy fractional integral equations (FFIE). We prove the existence of the solutions of FFIE under compactness type conditions using the Hausdorff measure of noncompactness. Also we prove an existence result without using noncompactness measure. For this we use a variant of the Schauder fixed point theorem in fuzzy metric space.