Both the Vikings and the Mamluks were skilled warriors known for their military prowess. They both established powerful empires through conquest and expansion.

Yes.

While the Russians did rise up against the Khanate of the Golden Horde (which controlled parts of what is now Russia and the "Stans" and proceeded to expand their territory by fighting the Khanate, the answer with the Mamluks needs more tweaking.

The Mamluks did exist during the time of the Abbassids. The Mamluks referred to Turkish slaves that eventually took up arms for themselves. They rose up against the Abbassids when they were weak and created their own government in the Levant and Egypt. Eventually, Ottomans defeated them and their forces became part of the Ottoman Empire's armies. The Mamluks rose up against Ottoman authority at a time (1700s) when the Ottomans were beginning to lose ground and prominence in Europe and the Janissaries were taking a larger stake in Imperial Affairs. This Mamluk Rebellion was swiftly crushed.

The Mamluks were the slave army of the Abbassids. They were often used to defend the Caliphate. Eventually, however, they rose up in revolt and created their own empires.

Egypt

As the empire expanded from being only Arabia, the political organization of Islam changed from being one governed by tribal codes and ethics to one with an imperial capital, provinces, and ostentatious royalty. Democracy and meritocracy were replaced with monarchy. A bureaucracy was developed in Damascus using former Sassanian and Byzantine talents. This is rather unique because in most empires, a conquered population was kept out of the ruling apparatus. However, in the Arab Empires, there was a strong intent to integrate the conquered populations and many in the territories wished to become Muslim due either to conviction or to financial incentive. The Maghreb, Spain, and Afghanistan were militarily annexed and there were expeditions (military) sent as far as Xinjiang Province (East Turkestan) is China. The empire was held together by institutions such as the governates, roads, and police/soldiers, just like every other empire. It just happens that track record of violence and repression is better for the Arab Empire than contemporaneous states.

The Muhammad Ali Dynasty was in control of Egypt for much of the 1800s. You will need to specify a more finite time period if you are looking for a particular Sultan, but the most famous of these was the man who spawned the dynasty, Muhammad Ali.

General Answer
NONE. Mongol horses were better trained and hardier horses than those used by the Mamluks. The reason that the Mamluks were able to prevail at the Battle of Ain Jalut was due to a better knowledge of the terrain, better tactics, secret alliances with the Christians that the Mongols were unaware of, superior numbers, and that the majority of the Mongols and their leader Hülegü Khan had recently departed from the front line for internal reasons in the Mongol Empire. While it is the case that the Mamluks used their horses to perform quicker maneuvers in the course of the battle, Mongol horses could have done those same moves, the Mongol riders simply chose not to employ that tactic.

Specifics on Why Mamluks Won
While better horses were not part of the reason for Mamluk victory, it is worth bearing down on some of the actual reasons for the Mamluk victory to understand why horse ability was irrelevant.

Immediately prior to the Battle of Ain Jalut two major things occurred that led to a fundamental change in the skill level and troop numbers on each side, negative for the Mongols and positive for the Mamluks: (1) Great Khan Möngke died and Hülegü Khan, the leader of the Mongol Forces in the Middle East and Möngke's brother, was required to return to Mongolia for a kurultai (vote for the next Great Khan) and brought the majority of his forces with him, leaving a smaller force under his lieutenant Kitbuqa. (2) Kipchak Türks fleeing west Turkestan (modern day west Kazakhstan) because they were a group that did not want to surrender to the Mongols found refuge with the Egyptian Mamluks and bolstered their numbers significantly.

When the battle started, the Mongols were caught off-guard, primarily because they did not expect for the Christian Crusaders to permit the Mamluks to cross over their lands to launch an attack on the Mongols, given the Crusaders' long abiding hatred of the "Saracen Mamluks". Once the battle had commenced, Baibar, the Mamluk general, used his extensive knowledge of the terrain in crafting his tactics and coordinating the battle. The battle had two major components; it started with a hit-and-run, where Baibar targeted Mongol cavalry and finished with a feint. A feint is where an army appears to retreat in defeat and the enemy pursues, usually in an attempt to rout the retreating army. However, the retreat is fake and leads the pursuing army into an ambush which they cannot handle as effectively since they are out of formation. This is exactly what happened, where after the Mongols pursued the falsely retreating Mamluks to the highlands, Mamluk forces emerged from hiding and began to fire arrows and attack with their cavalry. The Mongols were surrounded and defeated.

It was Hülegü Khan's intention to continue marching southwest towards Cairo to fight the Mamluk Sultanate in Egypt. He sent a threatening letter to the Mamluk Sultan Qutuz in Cairo, demanding that Qutuz surrender Cairo to the Mongols or it would be brutally razed as Baghdad and Damascus had been.

However, Hülegü was unable to fulfill this promise. The reason was that when the Great Khan of the Mongol Empire died, all of the potential new Great Khans needed to come to a great meeting in Mongolia called the kurultai. Since the recently deceased Great Khan was Möngke, Hülegü's brother, Hülegü was required to attend the kurultai. As a result, he departed for the kurultai in Mongolia and left behind only two tumens (20,000 men) in Syria under the leadership of his favorite general Naiman Kitbuqa Noyan. The Mamluks in Egypt and the lower Levant were able to ally and defeat these two remaining tumens in the Battle of Ain Jalut before Hülegü could return to the Middle East. (Hülegü's brother Kublai became the next Great Khan.)

Mamluks/mameluks (various spellings) were soldiers of slave origin in Muslim countries, some of whom achieved great status, e.g. Sultan.

(cf article in Wikipedia)

When the Abbassid Caliphate began to need to amass large armies for the maintenance of the empire, the Caliphs had two choices. One was to draft illiterate, bumbling peasant Arabs across the empire into one army or to enslave Türks from the "Stans" in Central Asia who had a general nomadic and warrior culture. The Caliphs chose the latter, enslaving hordes of Türks and bringing them back to be the army of the Caliphate. Because of their previous military experience, they did not need to be trained. These slave soldiers were called "Mamluk" (مملوك) which means "Owned One" or "Slave" in Arabic.

The Mamluks eventually gathered enough power to themselves to overthrow the Abbassid Caliphate and create their own states where they were the Sultans. In homage to their past, they kept the title Mamluk, even though they were now completely free.

Napoleon Bonaparte's French Campaign in Egypt and Syria (1798-1801) was meant to protect French trade interests, undermine Britain's access to India and establish scientific activity. Napoleon and his army were forced to withdraw after conflict in Europe, creating political disharmony in France and being defeated at the Battle of the Nile.

The main opposition that Napoleon's army had was from the Mamluk Sultanate that had power in Egypt and parts of the Levant. The Mamluks received naval support from the British.

Khedive Abbas II of Egypt was born on July 14, 1874 and died on December 19, 1944. Khedive Abbas II of Egypt would have been 70 years old at the time of death or 141 years old today.

Egypt.

The Mamluks successfully defeated the Mongol conquerors under the leadership of Kitbuqa (the second-in-command to Hülegü Khan) at the Battle of Ain Jalut in modern-day Israel.

When the Abbassid Caliphate began to need to amass large armies for the maintenance of the empire, the Caliphs had two choices. One was to draft illiterate, bumbling peasant Arabs across the empire into one army or to enslave Türks from the "Stans" in Central Asia who had a general nomadic and warrior culture. The Caliphs chose the latter, enslaving hordes of Türks and bringing them back to be the army of the Caliphate. Because of their previous military experience, they did not need to be trained. These slave soldiers were called "Mamluk" (مملوك) which means "Owned One" or "Slave" in Arabic.

The Mamluks eventually gathered enough power to themselves to overthrow the Abbassid Caliphate and create their own states where they were the Sultans. In homage to their past, they kept the title Mamluk, even though they were now completely free.

The Mongols, specifically at the Battle of Ain Jalut.