scholarly journals A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Separated Boundary Conditions ◽  
Fractional Differential

We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

scholarly journals Analysis of a coupled system of fractional differential equations with non-separated boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Danfeng Luo ◽  
Akbar Zada ◽  
Shaleena Shaleena ◽  
Manzoor Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Separated Boundary Conditions ◽  
Fractional Differential ◽  
Applied Fields ◽  
Rassias Stability

Abstract Solutions to fractional differential equations is an emerging part of current research, since such equations appear in different applied fields. A study of existence, uniqueness, and stability of solutions to a coupled system of fractional differential equations with non-separated boundary conditions is the main target of this paper. The existence and uniqueness results are obtained by employing the Leray–Schauder fixed point theorem and the Banach contraction principle. Additionally, we examine different types of stabilities in the sense of Ulam–Hyers such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. To prove the effectiveness of our main results, we study a few interesting examples.

Existence and uniqueness results for a class of BVPs for nonlinear fractional differential equations

2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Djamal Foukrach ◽  
Toufik Moussaoui ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Fractional Differential Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractThis paper studies some new existence and uniqueness results for boundary value problems for nonlinear fractional differential equations by using a variety of fixed point theorems. Some illustrative examples are also presented.

scholarly journals Existence and uniqueness of nonlocal boundary conditions for Hilfer–Hadamard-type fractional differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmad Y. A. Salamooni ◽  
D. D. Pawar
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlinear Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractIn this paper, we use some fixed point theorems in Banach space for studying the existence and uniqueness results for Hilfer–Hadamard-type fractional differential equations $$ {}_{\mathrm{H}}D^{\alpha ,\beta }x(t)+f\bigl(t,x(t)\bigr)=0 $$ D α , β H x ( t ) + f ( t , x ( t ) ) = 0 on the interval $(1,e]$ ( 1 , e ] with nonlinear boundary conditions $$ x(1+\epsilon )=\sum_{i=1}^{n-2}\nu _{i}x(\zeta _{i}),\qquad {}_{\mathrm{H}}D^{1,1}x(e)= \sum_{i=1}^{n-2} \sigma _{i}\, {}_{\mathrm{H}}D^{1,1}x( \zeta _{i}). $$ x ( 1 + ϵ ) = ∑ i = 1 n − 2 ν i x ( ζ i ) , H D 1 , 1 x ( e ) = ∑ i = 1 n − 2 σ i H D 1 , 1 x ( ζ i ) .

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 a Coupled System of Caputo-Hadamard Fractional Differential Equations with Nonlocal Hadamard Type Integral Boundary Conditions

2020 ◽  
Vol 4 (2) ◽  
pp. 13 ◽  
Author(s):  
Shorog Aljoudi ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we study a coupled system of Caputo-Hadamard type sequential fractional differential equations supplemented with nonlocal boundary conditions involving Hadamard fractional integrals. The sufficient criteria ensuring the existence and uniqueness of solutions for the given problem are obtained. We make use of the Leray-Schauder alternative and contraction mapping principle to derive the desired results. Illustrative examples for the main results are also presented.

scholarly journals Positive solutions for generalized two-term fractional differential equations with integral boundary conditions

2020 ◽  
Vol 1 (1) ◽  
pp. 47-63
Author(s):  
Hanan A. Wahash ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential

In this paper, we consider a class of boundary value problems for nonlinear two-term fractional differential equations with integral boundary conditions involving two $\psi $-Caputo fractional derivative. With the help of the properties Green function, the fixed point theorems of Schauder and Banach, and the method of upper and lower solutions, we derive the existence and uniqueness of positive solution of a proposed problem. Finally, an example is provided to illustrate the acquired results.

Sign in / Sign up

Export Citation Format

Share Document