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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Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion by Lin Hu, Siqing Gan

“…A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs) driven by Poisson processes. …”
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An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations by Dunqian Cao

“…Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. …”
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Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation by Mian Bahadur Zada, Muhammad Sarwar, Thabet Abdeljawad, Fahd Jarad

“…Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. …”
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A novel approach to $ \mathit{q} $-fractional partial differential equations: Unraveling solutions through semi-analytical methods by Khalid K. Ali, Mohamed S. Mohamed, M. Maneea

Subjects: “…$ \mathit{q} $-fractional partial differential equations…”
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A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation by Jun Zhou

“…We apply the result to give continuous dependence of solutions on initial data, derivative orders, and known functions for a fractional differential equation.…”
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The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions by Pedro Almenar, Lucas Jódar

“…This paper presents a method to obtain lower and upper bounds for the minimum distance between points a and b of the solution of the second order linear differential equation y′′+q(x)y=0 satisfying general separated boundary conditions of the type a11y(a)+a12y′(a)=0 and a21y(b)+a22y′(b)=0. …”
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Comparison Between Newton's Interpolation and Lagrange Method with Runge Kutt a Method in Solving First Order Differential Equations. by Muligi, Amos

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