During his scientific activity Nihan A. Aliev issued about 500 articles in international and local journals, made a speech and issued hundreds of articles in proceedings of conferences and congresses in English and Russian.
In 2020 year issued the study book with T.M. Aliyev and K.M. Jabiyev Secrets of finite and infinite quantities in Russian.
He is one of authors of study book Introduction to the Mathematical Logic issued in 2017.
He is also one of the authors of study book Fundamentals of Mathematical Analysis issued in 2016.
His book Discrete Additive Analysis issued in Persian in Islamic Republic of Iran in 1993. Then it is translated into English and issued as "Discrete Calculus By Analogy" on 3 Dec, 2009, in Toronto, Canada.
Within students he has investigated the solution of "One mixed problem" from the Theory of Elasticity under direction of Majid L. Rasulov. The result of this work is published in three pages in Rasulov's book named “Methods of contour integral”. This book was issued in Moscow (Russia) in 1964 by publishing house "Nauka", then translated and published in Holland in 1967.In those days he solved with his student (I. S. Zeinalov) "A certain Cauchy problem for two-dimensional equation of n-order with constant coefficient and homogeneous in the order of differentiation" with the method of residue. This work was issued in the journal of Differential Equations, 1965 in Minsk. (This journal is translated to English and now issuing in Moscow).
During post-graduate study he dealt with asymptotic of matrix-solutions of one system of ordinary linear differential first-order equations with matrix-coefficients depending on complex parameter. When the characteristic equation has multiple roots, in terms of Birkhof, asymptotic gets in terms of Tamarkin.
Then he worked on theory of boundary layer problems. Mathematic model of this problem is the boundary value problems, or Cauchy problems, for differential equations, containing higher derivatives with small parameter. In these problems were investigated sufficient conditions for existence or absence of boundary layer.
He also investigated the Cauchy problems and the boundary value problems for differential equations with fraction order and for differential equations where the order is changing in continuous manner.
In 1968-1972 years he worked at absence of solutions of boundary value problems. Absence of solutions was investigated in the following situations:
The first situation was examined by A.Lebeg. He proved in 1913, that for region like apple, the problem Dirikhle for Laplas equations doesn't have solutions. Later in 1924, he built the set of such regions.
Regarding to the second situation we can note the work of S.Kovalevskaya about Cauchy problem for differential equations with particular derivation, where she proved the existence and uniqueness of analytical solutions of Cauchy problem with analytical known. Then in 1946, in Сonference of mathematics I.G.Petrovskiy raised a question about solution in non-analytical case. G.Levi answered to this question in 1957, when he gave an example of linear, heterogeneous differential equation of first order in three-dimensional space with analytical coefficients, but with indefinitely differential (non-analytical) right side. In this case there is not even local solution. The class of such equations built L.Khermander and was awarded to Fildsov premium in 1962.
The third case for ordinary differential equation examined by A.A.Dezin and for Laplas equation with local boundary conditions examined by A.V.Bitsadze. But general linear non-local and global boundary conditions case examined by Nihan Aliev.
He gets the necessary conditions that help him to get sufficient conditions for Fredholm property of boundary value problems. When consider the boundary value problem for ordinary linear differential equation, the necessary conditions appear in the form of boundary conditions. When consider the partial differential equations, the necessary conditions appear in the form of non-local boundary conditions that also have the global items (i.e. integrals of borders and region). Therefore in the target setting he considers non-local boundary conditions. It gives him ability to consider the boundary value problem (for partial differential equation) for even and odd order. In classic research works (with local boundary conditions) were considered only equations of even order. For Laplas equation (of the second order) we need only one condition, but for biharmonic equation (of the fourth order) we must have two boundary conditions.