Further Developments of Bessel Functions via Conformable Calculus with Applications by Mahmoud Abul-Ez, Mohra Zayed, Ali Youssef

“…The theory of Bessel functions is a rich subject due to its essential role in providing solutions for differential equations associated with many applications. …”
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Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions by M. G. Sobamowo, A. T. Akinshilo, A. A. Yinusa

“…Similarity variables are used to transform the developed governing systems of nonlinear partial differential equations to systems of nonlinear ordinary differential equations. …”
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Asymptotic Comparison of the Solutions of Linear Time-Delay Systems with Point and Distributed Lags with Those of Their Limiting Equations by M. De la Sen

“…This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed) linear autonomous differential equations, and the associate ones of the corresponding perturbed functional differential equation. …”
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Homotopy Perturbation Method for Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Internal Heating and Variable Heat Flux by I-Chung Liu, Ahmed M. Megahed

“…Similarity transformations are used to transform the governing equations to a set of coupled nonlinear ordinary differential equations. The obtained differential equations are solved approximately by the homotopy perturbation method (HPM). …”
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Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect by Zuxiong Li, Xue Yang, Shengnan Fu

“…Further, by applying the bifurcation theory of impulsive differential equations, conditions under which the system has a positive periodic solution are obtained. …”
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Linearization from Complex Lie Point Transformations by Sajid Ali, M. Safdar, Asghar Qadir

“…Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension d, with d≤4. …”
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Rough Paths above Weierstrass Functions by Cellarosi, Francesco, Selk, Zachary

“…Rough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. …”
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Multiple Slip Effects on MHD Unsteady Flow Heat and Mass Transfer Impinging on Permeable Stretching Sheet with Radiation by Fazle Mabood, Stanford Shateyi

“…Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. …”
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High-Order Compact Implicit Difference Methods For Parabolic Equations in Geodynamo Simulation by Don Liu, Weijia Kuang, Andrew Tangborn

“…A series of compact implicit schemes of fourth and sixth orders are developed for solving differential equations involved in geodynamics simulations. …”
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Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications by Veli Shakhmurov

“…The infinite systems of the degenerate partial differential equations and Cauchy problem for system of parabolic equations are further studied in applications.…”
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Approximate Solutions of Fisher's Type Equations with Variable Coefficients by A. H. Bhrawy, M. A. Alghamdi

“…Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.…”
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Quasilinear Hyperbolic Systems Applied to Describe the Magnetohydrodynamic Nanofluid Flow by Dayong Nie

“…The influence of velocity slip on the flow and heat transfer properties of a hyperbolic nanofluid has been investigated. The partial differential equations for nanoparticle solid concentration, energy, and motion were turned into ordinary differential equations. …”
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Periodic Problems of Difference Equations and Ergodic Theory by B. A. Biletskyi, A. A. Boichuk, A. A. Pokutnyi

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Third-Order Approximate Solution of Chemical Reaction-Diffusion Brusselator System Using Optimal Homotopy Asymptotic Method by Salem Alkhalaf

“…It is observed that the method is easy to implement and quite valuable for handling nonlinear system of partial differential equations and yielding excellent results at minimum computational cost. …”
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CHAOS CONTROL OF PLANETARY GEAR TRAINBASED ON STRATEGY OF SPEED DISTURBANCE by WANG Juan, LI TongJie, JIN GuangHu, BAO HeYun

“…A new method called large parameter perturbation is used for the system that the differential equations are known and the allowance of speed disturbance is relatively big,and the speed is still selected as control parameter. …”
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Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation by Andrew Gratien Johnpillai, Chaudry Masood Khalique

“…These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. …”
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Evaluating a family of two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence by R. Bonciani, V. Del Duca, H. Frellesvig, J.M. Henn, M. Hidding, L. Maestri, F. Moriello, G. Salvatori, V.A. Smirnov

“…The computation of the integrals is performed with the method of differential equations. We provide a choice of basis for the polylogarithmic sectors, that puts the system of differential equations in canonical form. …”
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On expansions for nonlinear systems Error estimates and convergence issues by Beauchard, Karine, Le Borgne, Jérémy, Marbach, Frédéric

“…Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. …”
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ESTABLISHED MODES AND STATIC CHARACTERISTICS OF THREE-PHASE ASYNCHRONOUS MOTOR POWERED WITH SINGLE PHASE NETWORK by V. S. Malyar, V. V. Malyar

“…In order to perform it, the original nonlinear differential equations are algebraized by approximating the variables with the use of cubic splines. …”
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VIM for Solving the Pollution Problem of a System of Lakes by J. Biazar, M. Shahbala, H. Ebrahimi

“…Monitoring pollution is the first step toward planning to save the environment. The use of differential equations of monitoring pollution has become possible. …”
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