A New Generalized Chebyshev Matrix Algorithm for Solving Second-Order and Telegraph Partial Differential Equations by Waleed Mohamed Abd-Elhameed, Ramy M. Hafez, Anna Napoli, Ahmed Gamal Atta

“…This article proposes numerical algorithms for solving second-order and telegraph linear partial differential equations using a matrix approach that employs certain generalized Chebyshev polynomials as basis functions. …”
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Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation by Qian Guo, Xueyin Tao

“…The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in Lp-sense. …”
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Existence and Uniqueness of Positive Solutions to Nonlinear Second Order Impulsive Differential Equations with Concave or Convex Nonlinearities by Lingling Zhang, Chengbo Zhai

“…Using a new fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to nonlinear two-point boundary value problems for second-order impulsive differential equations with concave or convex nonlinearities.…”
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Existence and Stability for a Coupled Hybrid System of Fractional Differential Equations with Atangana–Baleanu–Caputo Derivative by Liyuan Zhao, Yirong Jiang

“…The aim of this article is to investigate a coupled hybrid system of fractional differential equations with the Atangana–Baleanu–Caputo derivative which contains a Mittag–Leffler kernel function in its kernel. …”
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Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations by Kifayat Ullah, Sabri T. M. Thabet, Anwar Kamal, Junaid Ahmad, Fayyaz Ahmad

“…An application to solve a fractional differential equation (FDE) is also provided. It has been eventually shown that the K∗- iterative process of this example gives more accurate numerical results corresponding to some other iterative processes of the literature. …”
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A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations by Yanli Zhou, Yonghong Wu, Xiangyu Ge, B. Wiwatanapataphee

“…Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. …”
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Existence and Uniqueness Results for Hadamard-Type Fractional Differential Equations with Nonlocal Fractional Integral Boundary Conditions by Phollakrit Thiramanus, Sotiris K. Ntouyas, Jessada Tariboon

“…We study the existence and uniqueness of solutions for a fractional boundary value problem involving Hadamard-type fractional differential equations and nonlocal fractional integral boundary conditions. …”
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New Operational Matrix via Genocchi Polynomials for Solving Fredholm-Volterra Fractional Integro-Differential Equations by Jian Rong Loh, Chang Phang, Abdulnasir Isah

“…In this paper, we apply a new operational matrix via Genocchi polynomials to solve fractional integro-differential equations (FIDEs). We also derive the expressions for computing Genocchi coefficients of the integral kernel and for the integral of product of two Genocchi polynomials. …”
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A Coupling Method of New EMFE and FE for Fourth-Order Partial Differential Equation of Parabolic Type by Yang Liu, Hong Li, Zhichao Fang, Siriguleng He, Jinfeng Wang

“…We propose and analyze a new numerical method, called a coupling method based on a new expanded mixed finite element (EMFE) and finite element (FE), for fourth-order partial differential equation of parabolic type. We first reduce the fourth-order parabolic equation to a coupled system of second-order equations and then solve a second-order equation by FE method and approximate the other one by a new EMFE method. …”
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Solution of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels by R. K. Saxena, S. L. Kalla

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Solving a system of Caputo-Hadamard fractional differential equations via Perov’s fixed point theorem by Nouar Aziza Souad, Nisse Khadidja, Beloul Said

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LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions by Xueyan Zhao, Feiqi Deng, Xiaojing Zhong

“…We investigate LaSalle-type theorems for general nonlinear stochastic functional differential equations. With some preliminaries on lemmas and the derivation techniques, we establish three LaSalle-type theorems for the general nonlinear stochastic functional differential equations via multiple Lyapunov functions. …”
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Approximate analytical solution of a class of highly nonlinear time–fractional-order partial differential equations by Richard Olu Awonusika

“…Partial Differential Equations in Applied Mathematics…”
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Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative by Muath Awadalla, Yves Yannick Yameni Noupoue, Kinda Abu Asbeh, Noureddine Ghiloufi

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Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems by Yongqing Wang

“…In this paper, we consider a class of fractional differential equations with conjugate type integral conditions. …”
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A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition by Mohamed Jleli, Lakhdar Ragoub, Bessem Samet

“…We establish a new Lyapunov-type inequality for a class of fractional differential equations under Robin boundary conditions. The obtained inequality is used to obtain an interval where a linear combination of certain Mittag-Leffler functions has no real zeros.…”
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Investigation of Behavior on Solutions of Lane–Emden Complex Differential Equations by a Random Differential Transformation Method by Mehmet Merdan, Merve Merdan, Rıdvan Şahin

“…In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of complex differential equations. …”
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Evolutionary Stability Analysis of the Coal Mine Safety Management System Governed by Delay and Impulsive Differential Equations by Li Bai, Xinhua Wang, Rongwu Lu, Hao Yu, Dan Li

“…To study the regular pattern of behavior propagations in CMSM, a series of evolutionary dynamical system models are established by the delay and impulsive differential equations (DIDEs). The threshold constraints (TCs) and impulse responses in the models can accurately correspond to the actual inspection and supervision measures in safety management. …”
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Solutions of Systems of " Order Ordinary Differential Equations Using the Combined Laplace Transform-Adomian Decomposition Method. by Byamukama, Justus

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Global solution for wave equation involving the fractional Laplacian with logarithmic nonlinearity by Bidi Younes, Abderrahmane Beniani, Khaled Zennir, Zayd Hajjej, Hongwei Zhang

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