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Special Issue: Nonlinear Differential Equations: Oscillation Theory, Methods and Applications

Guest Editor

Prof. Dr. Omar Bazighifan
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen
Email: o.bazighifan@gmail.com
Interests: qualitative theory; ordinary differential equations; fractional differential equations; dynamical systems; mathematical modeling

Manuscript Topics

Ordinary, fractional and partial differential equations are universally recognized as powerful tools to model and solve practical problems involving nonlinear phenomena. In particular, we mention physical processes as problems in elasticity theory, where we deal with composites made of two different materials with different hardening exponents.
Therefore, the theory of differential equations has been successfully applied to establish the existence and multiplicity of solutions of boundary value problems via direct methods, minimax theorems, variational methods, and topological methods. If possible, one looks towards solutions in special forms by using the symmetries of the driving equation. This also leads to the study of the difference counterparts of such equations to provide exact or approximate solutions. We mention the reduction methods for establishing exact solutions as solutions of lower-dimensional equations.


Keywords:
Mathematical modeling techniques
Qualitative properties of solutions
Oscillation theory
Delay differential equations
Ordinary differential/difference equations
Numerical solutions
Partial/functional equations
Fractional differential and integral calculus
Applications
This Special Issue will accept high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology.


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Please submit your manuscript to online submission system    
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Paper Submission

All manuscripts will be peer-reviewed before their acceptance for publication. The deadline for manuscript submission is 31 August 2025

Published Papers(12)

Research article
Dynamics of Lie symmetry, Paul-Painlevé approach, bifurcation aalysis to the Ivancevic option pricing model via a optimal system of Lie subalgebra
Ibtehal Alazman
2025, Volume 10, Issue 4: 8965-8987. doi: 10.3934/math.2025411
Abstract HTML PDF Viewed (248)
Research article
Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise
Siru Li Tian Xu Ailong Wu
2025, Volume 10, Issue 3: 6379-6405. doi: 10.3934/math.2025291
Abstract HTML PDF Viewed (230)
Research article
Exact and numerical solutions of the generalized breaking soliton system: Insights into non-linear wave dynamics
Amer Ahmed Abdulghani R. Alharbi Ishak Hashim
2025, Volume 10, Issue 3: 5124-5142. doi: 10.3934/math.2025235
Abstract HTML PDF Cited (1) Viewed (378)
Research article
On nonlinear coupled differential equations for corrugated backward facing step (CBFS) with circular obstacle: AI-neural networking
Khalil Ur Rehman Wasfi Shatanawi Weam G. Alharbi
2025, Volume 10, Issue 3: 4579-4597. doi: 10.3934/math.2025212
Abstract HTML PDF Cited (1) Viewed (428)
Research article
Second-order advanced dynamic equations on time scales: Oscillation analysis via monotonicity properties
Samy E. Affan Elmetwally M. Elabbasy Bassant M. El-Matary Taher S. Hassan Ahmed M. Hassan
2025, Volume 10, Issue 2: 4473-4491. doi: 10.3934/math.2025206
Abstract HTML PDF Viewed (383)
Research article
Existence and uniqueness of solutions for a class of fractional differential equation with lower-order derivative dependence
Yujun Cui Chunyu Liang Yumei Zou
2025, Volume 10, Issue 2: 3797-3818. doi: 10.3934/math.2025176
Abstract HTML PDF Viewed (426)
Research article
Nonlinear neutral differential equations of second-order: Oscillatory properties
Maged Alkilayh
2025, Volume 10, Issue 1: 1589-1601. doi: 10.3934/math.2025073
Abstract HTML PDF Viewed (794)
Research article
Some new oscillation results for second-order differential equations with neutral term
Abdullah Mohammed Alomair Ali Muhib
2025, Volume 10, Issue 1: 694-704. doi: 10.3934/math.2025031
Abstract HTML PDF Viewed (727)
Research article
Nonlinear differential equations with neutral term: Asymptotic behavior of solutions
Maryam AlKandari
2024, Volume 9, Issue 12: 33649-33661. doi: 10.3934/math.20241606
Abstract HTML PDF Viewed (810)
Research article
On The oscillatory behavior of solutions to a class of second-order nonlinear differential equations
Maged Alkilayh
2024, Volume 9, Issue 12: 36191-36201. doi: 10.3934/math.20241718
Abstract HTML PDF Viewed (725)
Research article
Improving diversification by a hybrid bat-Nelder-Mead algorithm and DDE for rapid convergence to solve global optimization
Enas Suhail Mahmoud El-Alem Omar Bazighifan Ahmed Zekri
2024, Volume 9, Issue 12: 35655-35677. doi: 10.3934/math.20241692
Abstract HTML PDF Viewed (591)
Research article
Optimal homotopy analysis method for (2+1) time-fractional nonlinear biological population model using $ {{J}} $-transform
Khalid K. Ali Mohamed S. Mohamed M. Maneea
2024, Volume 9, Issue 11: 32757-32781. doi: 10.3934/math.20241567
Abstract HTML PDF Viewed (687)