Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations by Jagdev Singh, Devendra Kumar, Adem Kılıçman

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Results on Uniqueness of Solution of Nonhomogeneous Impulsive Retarded Equation Using the Generalized Ordinary Differential Equation by D. K. Igobi, U. Abasiekwere

“…International Journal of Differential Equations…”
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Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations by Jafar Biazar, Mohammad Hosami

“…International Journal of Differential Equations…”
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Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima” by S. Hristova, A. Golev

“…The object of investigation of the paper is a special type of functional differential equations containing the maximum value of the unknown function over a past time interval. …”
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Some maximum principles for solutions of a class of partial differential equations in Ω⊂ℝn by Mohammad Mujalli Al-Mahameed

“…We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1) Δ2u+αf(u)=0, α∈ℝ+ and (2) ΔΔu+α(Δu)k+gu=0, α≤0 in some region Ω⊂ℝn.…”
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A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations by Shehu Maitama

“…International Journal of Differential Equations…”
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Problem Involving the Riemann–Liouville Derivative and Implicit Variable-Order Nonlinear Fractional Differential Equations by Zoubida Bouazza, Mohammed Said Souid, Hatıra Günerhan, Ali Shokri

“…The problem of boundary values for implicit differential equations with nonlinear fractions involving the variable order and the Riemann–Liouville derivative is examined in this article along with its existence and stability. …”
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An Extension of the Double G′/G, 1/G-Expansion Method for Conformable Fractional Differential Equations by Altaf A. Al-Shawba, Farah A. Abdullah, Amirah Azmi, M. Ali Akbar

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Nonexplosion and Pathwise Uniqueness of Stochastic Differential Equation Driven by Continuous Semimartingale with Non-Lipschitz Coefficients by Jinxia Wang

“…We study a class of stochastic differential equations driven by semimartingale with non-Lipschitz coefficients. …”
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New Results for Some Intuitionistic Fuzzy Partial Functional Differential Equations with State-Dependent Delay by Bouchra Ben Amma, Said Melliani, Lalla Saadia Chadli

Subjects: “…partial functional differential equations…”
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Spectral Criteria for Solvability of Boundary Value Problems and Positivity of Solutions of Time-Fractional Differential Equations by Valentin Keyantuo, Carlos Lizama, Mahamadi Warma

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Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate by Dany Joy, Dinesh Kumar S, Fathalla A Rihan

“…Abstract This work introduces a numerical technique designed to efficiently solve a specific type of differential equations known as a weakly coupled system of singularly perturbed delay differential equations. …”
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On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations by S. S. Motsa

“…This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. …”
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Boundary Value Problem for Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Impulses by Abdelkrim Salim, Mouffak Benchohra, Jamal Eddine Lazreg, Gaston N’Guérékata

“…This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. …”
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Existence of C1-Positive Solutions for a Class of Second-Order Impulsive Differential Equations by Hong Li

“…In this study, under some inequality conditions, necessary and sufficient conditions, using fixed-point theorem in cones, are established for the existence of C1-positive solutions for a class of second-order impulsive differential equations. Two examples are given in the last section to illustrate the abstract results.…”
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Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces by Yulin Zhao, Li Huang, Xuebin Wang, Xianyang Zhu

“…By means of the fixed-point theorem in the cone of strict-set-contraction operators, we consider the existence of a nonlinear multi-point boundary value problem of fractional integro-differential equation in a Banach space. In addition, an example to illustrate the main results is given.…”
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Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations

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Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients by Hui Yu, Minghui Song

“…The numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. …”
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Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions by Said R. Grace, Gokula N. Chhatria, S. Kaleeswari, Yousef Alnafisah, Osama Moaaz

Subjects: “…differential equation…”
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Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations by Mujeeb Ur Rehman, Rahmat Ali Khan

“…We study existence of positive solutions to nonlinear higher-order nonlocal boundary value problems corresponding to fractional differential equation of the type 𝑐𝒟𝛿0+𝑢(𝑡)+𝑓(𝑡,𝑢(𝑡))=0, 𝑡∈(0,1), 0<𝑡<1. 𝑢(1)=𝛽𝑢(𝜂)+𝜆2, 𝑢(0)=𝛼𝑢(𝜂)−𝜆1, 𝑢(0)=0, 𝑢(0)=0⋯𝑢(𝑛−1)(0)=0, where, 𝑛−1<𝛿<𝑛, 𝑛(≥3)∈ℕ, 0<𝜂,𝛼,𝛽<1, the boundary parameters 𝜆1,𝜆2∈ℝ+ and 𝑐𝐷𝛿0+ is the Caputo fractional derivative. …”
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