On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative by Abduljawad Anwar, Shayma Adil Murad

Subjects: “…fractional differential equations $ ({\mathcal{fde}}{s}) $…”
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Existence and Uniqueness Results for Two-Term Nonlinear Fractional Differential Equations via a Fixed Point Technique by H. R. Marasi, H. Aydi

“…The work addressed in this paper is to ensure the existence and uniqueness of positive solutions for initial value problems for nonlinear fractional differential equations with two terms of fractional orders. …”
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On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations by Haiyan Yuan, Jihong Shen, Cheng Song

“…A split-step theta (SST) method is introduced and used to solve the nonlinear neutral stochastic delay differential equations (NSDDEs). The mean square asymptotic stability of the split-step theta (SST) method for nonlinear neutral stochastic delay differential equations is studied. …”
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A traffic prediction method for missing data scenarios: graph convolutional recurrent ordinary differential equation network by Ming Jiang, Zhiwei Liu, Yan Xu

Subjects: “…Neural ordinary differential equation…”
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The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation by Qian Guo, Xueyin Tao

“…Almost sure exponential stability of the split-step backward Euler (SSBE) method applied to an Itô-type stochastic differential equation with time-varying delay is discussed by the techniques based on Doob-Mayer decomposition and semimartingale convergence theorem. …”
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Positive Solutions for Fractional Differential Equations from Real Estate Asset Securitization via New Fixed Point Theorem by Hao Tao, Meichen Fu, Ru Qian

“…We study a fractional differential equation dynamics model arising from the analysis of real estate asset securitization by using the generalized fixed point theorem for weakly contractive mappings in partially ordered sets. …”
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Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems by M. P. Markakis

“…International Journal of Differential Equations…”
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Constructive Existence of (1,1)-Solutions to Two-Point Value Problems for Fuzzy Linear Multiterm Fractional Differential Equations by HuiChol Choi, SungHyok Kwon, Kinam Sin, Sunae Pak, Sungryol So

“…In this paper, we consider the following two-point boundary value problems of fuzzy linear fractional differential equations: (Dc1,1αy)(t)⊕b(t)⊗(Dc1,1βy)(t)⊕c(t)⊗y(t)=f(t), t∈(0,1), y(0)=y0 and y(1)=y1, where b,c∈C(I), b(t),c(t)≥0, y,f∈C(I,RF), I=[0,1], y0,y1∈RF and 1<β<α≤2. …”
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Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology by Heiko Enderling, Alexander R.A. Anderson, Mark A.J. Chaplain, Glenn W.A. Rowe

Subjects: “…partial differential equations…”
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Solving class of mixed nonlinear multi-term fractional Volterra-Fredholm integro-differential equations by new development of HAM by Zainidin Eshkuvatov, Zaid Laadjal, Shahrina Ismail

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Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods by Zainab Olabisi Dere, Gbeminiyi Musibau Sobamowo, Antonio Marcos de Oliveira Siqueira

Subjects: “…Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method.…”
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Corrigendum to “A Three-Point Boundary Value Problem with an Integral Condition for a Third-Order Partial Differential Equation” by C. Latrous, A. Memou

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An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula by Kaori Okuma

“…This paper introduces an asymptotic expansion for the smooth solution of a semi-linear partial differential equation. Our scheme is based on Itô’s formula, Taylor’s expansion, nonlinear Feynman–Kac formula and some algebras.…”
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Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving ψ-Hilfer Fractional Derivatives by Athasit Wongcharoen, Sotiris K. Ntouyas, Phollakrit Wongsantisuk, Jessada Tariboon

“…In this article, we discuss the existence and uniqueness of solutions for a new class of coupled system of sequential fractional differential equations involving ψ-Hilfer fractional derivatives, supplemented with multipoint boundary conditions. …”
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A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay by Prabakaran Raghavendran, Tharmalingam Gunasekar, Junaid Ahmad, Walid Emam

“…This paper presents an analysis of the existence, uniqueness, and stability of solutions to fractional neutral Volterra-Fredholm integro-differential equations, incorporating Caputo fractional derivatives and semigroup operators with state-dependent delays. …”
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Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method by Ömer Faruh Gözükızıl, Hami Gündoğdu

“…And then, the inhomogeneous Boussinesq equation and another nonlinear partial differential equation subject to given initial values are solved by using LDM. …”
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Novel exploration of topological degree method for noninstantaneous impulsive fractional integro-differential equation through the application of filtering system by Kanagaraj Muthuselvan, Baskar Sundaravadivoo, Shankar Rao Munjam, Kottakkaran Sooppy Nisar

Subjects: “…Fractional differential equation…”
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Newmark-FDTD Formulation for Modified Lorentz Dispersive Medium and Its Equivalence to Auxiliary Differential Equation-FDTD with Bilinear Transformation by Hongjin Choi, Jeahoon Cho, Yong Bae Park, Kyung-Young Jung

“…The Newmark-FDTD method was recently proposed for the EM analysis of dispersive media and it was shown that the proposed Newmark-FDTD method can give higher stability and better accuracy compared to the conventional auxiliary differential equation- (ADE-) FDTD method. In this work, we extend the Newmark-FDTD method to modified Lorentz medium, which can simply unify aforementioned dispersion models. …”
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Stability of Perturbed Set Differential Equations Involving Causal Operators in Regard to Their Unperturbed Ones considering Difference in Initial Conditions by Coșkun Yakar, Hazm Talab

“…We investigate the stability of solutions of perturbed set differential equations with causal operators in regard to their corresponding unperturbed ones considering the difference in initial conditions (time and position) by utilizing Lyapunov functions and Lyapunov functionals.…”
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Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel by M. Taghipour, H. Aminikhah

“…This article focuses on finding the numerical solution of the nonlinear time–fractional partial integro–differential equation. For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative, nonlinear, and integro–differential terms; and by collocation points, we transform the problem to a system of nonlinear equations. …”
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