I've been reading alot about the Abbasid Caliphate and discovered that, despite it's high amount of growth and innovation, it was simultaneously socially and economically unstable right from the get go which in turn lead to a great and slow stagnation. The Abbasids were simply too unprepared to handle the torch which the Umayyads held. Now after realizing this, I made a hypothesis that the decadency of the Abbasid Caliphate may have contributed to not only it's lack of economic development and social stability, but also to the events that lead to it's demise. The Mongol invasion, the Mu'tazila's political brutality, the Ash'ari's well-meaning but consequential beliefs, and the lack of utilizing any inventions made by their own citizens (the Umayyad Dynasty would've certainly made greater use of torpedoes than the Abbasids) could've all been avoided by a smarter and more capable Abbasid regime.
So I challenge all of you to figure out a way in which the Abbasid Caliphate can become more stable and less decadent than it is in our timeline. I particularly address this challenge to all Islamic or Middle Eastern historical experts.
I'm not entirely sure I agree with the premise here. Suggesting that the 'Abbasid Caliphate was socially and economically unstable from it's inception seems like a stretch, considering the longevity of the entity (consider, especially, compared to the Umayyads or any contemporary Byzantine dynasties, and it does exceptionally well in time alone), and attributing this to "decadence" smells a bit orientalist to me. I would also challenge the assertion that the Umayyads would inherently have made better use of technology such as torpedoes - sure, in some TLs that may be the case, but I'm not certain that's an inevitability. Not to suggest that you're misrepresenting 'Abbasid history, of course - they were indeed unstable, particularly in the latter half of their reign (945 on) due to the rise of military strongmen in the Buyids, Fatimids, Seljuqs, and ultimately Mongols who could match them. But while certain elements of the erosion of 'Abbasid military power in favor of those strongmen - which I think the Mu'tazilite fall from grace is absolutely a part of - has less to do with a generalized "decadence" and more with the shifting notions of what the title of
Khalifa meant and what powers were associated with it, as well as the simple cyclical nature of the loss of power in taxpaying regions reducing the Caliphate's ability to project power in the remaining taxpaying regions, and so on.
Basically, I contend that the rise of military strongmen who upset the stability of the 'Abbasid Caliphate was due in part to an ideological divide created by the question of the Caliphate as an elected or appointed position, as well as other theological divides that are not necessarily caused by poor leadership or decadence, but merely inherent to any organized religion, that nonetheless effected the 'Abbasids due to their dual role as political leader and religious heads. That combined with the geopolitical and demographic reality of their location, which made them targets for intervention from more warlike groups on their fringes, of which the Seljuqs and Mongols are the most notable. In other words, I'd reject the notion that any one family is essentially anything, including decadent, and instead assert that any instability inherent to the 'Abbasid Caliphate was created by institutional and geographic forces.
So, to answer your original question of making a more stable 'Abbasid Caliphate, I would want to avoid the hiring of any armies or guard units composed exclusively of one group of people, and instead integrate a variety of peoples and political factions across the military, so that one group cannot use an advantageous position to try and usurp control over the Caliphate. That should help avoid the Anarchy at Samarra, which in turn should head off the tendency of far-flung provinces to fall under the sway of local strongmen and reduce the power at the center. If that, in turn, could preserve a centrally powerful Caliphate capable of turning back the Seljuqs, then I'd want to take a look at their dual status as successors to the prophet and emperors of a massive, multi-ethnic empire ruled on the legitimacy of their faith. That'd take some legalistic and theological wrangling that I'm not really equipped for, but it's a start.
I hope I'm not coming off as hostile to your question, I just wanted to clarify a few things from my own reading of histories on the topic.