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Nonlocal Extensions of First Order Initial Value Problems

Axioms
We study certain Volterra integral equations that extend and recover first order ordinary differential equations (ODEs). We formulate the former equations from the latter by replacing classical derivatives with nonlocal integral operators with anti ...
Ravi Shankar
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Initial value problems for fractional functional differential inclusions with Hadamard type derivatives in Banach spaces [PDF]

Surveys in Mathematics and its Applications, 2018
The authors establish sufficient conditions for the existence of solutions to boundary value problems for fractional differential inclusions involving the Hadamard type derivatives of order α ∈ (0,1] in Banach spaces.
John R. Graef, Nassim Guerraiche, Samira Hamani   +2 more
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The Solutions of Initial (-Boundary) Value Problems for Sharma-Tasso-Olver Equation

Mathematics, 2022
A nonlinear transformation from the solution of linear KdV equation to the solution of Sharma-Tasso-Olver (STO) equation is derived out by using simplified homogeneous balance (SHB) method.
Lingxiao Li, Mingliang Wang, Jinliang Zhang   +2 more
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Nonlinear singular hyperbolic initial boundary value problems

Electronic Journal of Differential Equations, 2017
In this article, we aim to prove the well posedness of a one point initial boundary value problem for a nonlinear hyperbolic singular integro-differential partial differential equation.
Said Mesloub, Imed Bachar
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Solvability of singular second-order initial value problems

Electronic Journal of Differential Equations, 2016
This article concerns the solvability of the initial-value problem x''=f(t,x,x'), x(0)=A, x'(0)=B, where the scalar function f may be unbounded as $t\to 0$.
Petio Kelevedjiev
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Solution dependence on problem parameters for initial-value problems associated with the Stieltjes Sturm-Liouville equations

Electronic Journal of Differential Equations, 2005
We examine properties of solutions to a 2n-dimensional Stieltjes Sturm-Liouville initial-value problem. Existence and uniqueness of a solution has been previously proven, but we present a proof in order to establish properties of boundedness, bounded ...
Laurie Battle
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Initial Boundary Value Problems of Semi-Linear Sub-Diffusion with Gradient Terms

Mathematics, 2020
We consider the existence and uniqueness of the saturated classical solutions and the positive classical solutions to initial boundary value problems of semi-linear sub-diffusion with gradient terms. Applying this to the fractional power of the sectorial
Yabing Gao, Yongxiang Li
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Initial-boundary value problems for the wave equation

Electronic Journal of Differential Equations, 2014
In this work we consider an initial-boundary value problem for the one-dimensional wave equation. We prove the uniqueness of the solution and show that the solution coincides with the wave potential.
Tynysbek Sh. Kalmenov, Durvudkhan Suragan   +1 more
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Nonlinear initial-value problems with positive global solutions

Electronic Journal of Differential Equations, 2003
We give conditions on $m(t)$, $p(t)$, and $f(t,y,z)$ so that the nonlinear initial-value problem {gather*} frac{1}{m(t)} (p(t)y')' + f(t,y,p(t)y') = 0,quadmbox{for }t>0, y(0)=0,quad lim_{t o 0^+} p(t)y'(t) = B, end{gather*} has at least one positive ...
John V. Baxley, Cynthia G. Enloe
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Initial value problems

Scholarpedia, 2007
Lawrence F. Shampine, Skip Thompson
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