scholarly journals Existence and uniqueness results for a class of fractional differential equations with an integral fractional boundary condition

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1241-1249 ◽  
Author(s):  
Asghar Ahmadkhanlu
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Necessary Conditions ◽  
Boundary Value ◽  
Fractional Order Differential Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Sufficient And Necessary Conditions ◽  
Fractional Differential

The aim of this work is to study a class of boundary value problem including a fractional order differential equation. Sufficient and necessary conditions will be presented for the existence and uniqueness of solution of this fractional boundary value problem.

scholarly journals On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1899
Author(s):  
Ahmed Alsaedi ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Liouville Type ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we derive existence and uniqueness results for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential boundary value problem with multi-point sub-strip boundary conditions, via Banach and Krasnosel’skii⏝’s fixed point theorems. Examples are included for the illustration of the obtained results.

scholarly journals Existence and uniqueness results for fractional Navier boundary value problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Imed Bachar ◽  
Hassan Eltayeb
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Operator Equation ◽  
Real Function ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Alpha Beta

Abstract We establish the existence, uniqueness, and positivity for the fractional Navier boundary value problem: $$\begin{aligned} \textstyle\begin{cases} D^{\alpha }(D^{\beta }\omega )(t)=h(t,\omega (t),D^{\beta }\omega (t)), & 0< t< 1, \\ \omega (0)=\omega (1)=D^{\beta }\omega (0)=D^{\beta }\omega (1)=0, \end{cases}\displaystyle \end{aligned}$$ { D α ( D β ω ) ( t ) = h ( t , ω ( t ) , D β ω ( t ) ) , 0 < t < 1 , ω ( 0 ) = ω ( 1 ) = D β ω ( 0 ) = D β ω ( 1 ) = 0 , where $\alpha,\beta \in (1,2]$ α , β ∈ ( 1 , 2 ] , $D^{\alpha }$ D α and $D^{\beta }$ D β are the Riemann–Liouville fractional derivatives. The nonlinear real function h is supposed to be continuous on $[0,1]\times \mathbb{R\times R}$ [ 0 , 1 ] × R × R and satisfy appropriate conditions. Our approach consists in reducing the problem to an operator equation and then applying known results. We provide an approximation of the solution. Our results extend those obtained in (Dang et al. in Numer. Algorithms 76(2):427–439, 2017) to the fractional setting.

scholarly journals Integral Boundary Value Problems for Implicit Fractional Differential Equations Involving Hadamard and Caputo-Hadamard fractional Derivatives

2021 ◽  
Vol 45 (03) ◽  
pp. 331-341
Author(s):  
P. KARTHIKEYAN ◽  
R. ARUL
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Implicit Fractional Differential Equations

In this paper, we examine the existence and uniqueness of integral boundary value problem for implicit fractional differential equations (IFDE’s) involving Hadamard and Caputo-Hadamard fractional derivative. We prove the existence and uniqueness results by utilizing Banach and Schauder’s fixed point theorem. Finally, examples are introduced of our results.

scholarly journals Dirichlet Problem for Maximal Graphs of Higher Codimension

2020 ◽  
Author(s):  
Yang Li
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
General Existence

Abstract We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian-type ambient spaces and obtain general existence and uniqueness results that apply to any codimension.

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