Generalized Boundary Conditions in an Existence and Uniqueness Proof for the Solution of the Non-Stationary Electron Boltzmann Equation by Means of Operator-Semigroups

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

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On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽

10.3390/math8040476 ◽

2020 ◽

Vol 8 (4) ◽

pp. 476

Author(s):

Jiraporn Reunsumrit ◽

Thanin Sitthiwirattham

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Difference Equations ◽

Existence And Uniqueness ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

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Existence and uniqueness results for a nonlinear coupled system involving Caputo fractional derivatives with a new kind of coupled boundary conditions

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107018 ◽

2021 ◽

pp. 107018

Author(s):

Bashir Ahmad ◽

Madeaha Alghanmi ◽

Ahmed Alsaedi ◽

Juan J. Nieto

Keyword(s):

Boundary Conditions ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Coupled System ◽

Caputo Fractional Derivatives ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Nonlinear Coupled System ◽

Coupled Boundary Conditions

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On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

Mathematics ◽

10.3390/math9111205 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1205

Author(s):

Usman Riaz ◽

Akbar Zada ◽

Zeeshan Ali ◽

Ioan-Lucian Popa ◽

Shahram Rezapour ◽

...

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Boundary Conditions ◽

Coupled System ◽

Initial Boundary ◽

Liouville Type ◽

Liouville Derivative ◽

Banach Contraction ◽

Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.

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