The biological models for the study of human immunodeficiency virus (HIV) and its advanced stage acquired immune deficiency syndrome (AIDS) have been widely studied in last two decades. HIV virus can be transmitted by different means including blood, semen, preseminal fluid, rectal fluid, breast milk, and many more. Therefore, initiating HIV treatment with the TB treatment development has some advantages including less HIV‐related losses and an inferior risk of HIV spread also having difficulties including incidence of immune reconstitution inflammatory syndrome (IRIS) because of a large pill encumbrance. It has been analyzed that patients with HIV have more weaker immune system and are susceptible to infections, for example, tuberculosis (TB). Keeping the importance of the HIV models, we are interested to consider an analysis of HIV‐TB coinfected model in the Atangana‐Baleanu fractional differential form. The model is studied for the existence, uniqueness of solution, Hyers‐Ulam (HU) stability and numerical simulations with assumption of specific parameters.

We deal with three important aspects of a generalized impulsive fractional order differential equation (DE) involving a nonlinear p-Laplacian operator: the existence of a solution, the uniqueness and the Hyers-Ulam stability. Our problem involves Caputo's fractional derivative. For these goals, we establish an equivalent fractional integral form of the problem and use a topological degree approach for the existence and uniqueness of the solution (EUS). Next, we check the stability of the suggested problem and then demonstrate the results via an illustrative example. In the literature, we could not find articles on the Hyers-Ulam stability of the impulsive fractional order DEs with φ p operator.

Recently, AB-fractional calculus has been introduced by Atangana and Baleanu and attracted a large number of scientists in different scientific fields for the exploration of diverse topics. An interesting aspect is the generalization of classical inequalities via AB-fractional integral operators. In this paper, we aim to generalize Minkowski inequality using the AB-fractional integral operator.

In this paper, we are dealing with an analytical study of a singular fractional order nonlinear differential equation with fractional integral and differential boundary conditions and p -operator, for existence and stability results. Our problem is based on two types of fractional order derivatives, that is, Caputo factional derivative of order and Riemann-Liouville derivative of order , where m − 1 < , ≤ m, and m ∈ {3, 4, 5, … }. The suggested problem will be converted into an equivalent integral form by the help of Green function. After the proofs for these properties, some classical fixed point theorems are employed for the existence of positive solution (EPS). For application of the results, an expressive example is included. KEYWORDS Caputo fractional derivative, existence of positive solution, Hyers-Ulam stability, Riemann-Liouville fractional derivative, singular fractional differential equations c  u(t) = u(t) + (t, u(t)), u ′ (t) = 0, u(0) = h(u(T)), where 0 < T < +∞,  ∈ R + , , h are given functions and c  is Caputo derivative of fractional order ∈ (1, 2). Baleanu et al 15 studied EUS for the following equation: Math Meth Appl Sci. 2018;41:9321-9334.wileyonlinelibrary.com/journal/mma existence results for a class of nonlinear fractional differential equations with singularity. Math Meth Appl Sci. 2018;41:9321-9334.

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