scholarly journals Fractional-Order Integro-Differential Multivalued Problems with Fixed and Nonlocal Anti-Periodic Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1774 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Ravi P. Agarwal ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Caputo Fractional Derivatives ◽  
New Class ◽  
Fractional Differential ◽  
The Given ◽  
Derivatives Of

This paper studies a new class of fractional differential inclusions involving two Caputo fractional derivatives of different orders and a Riemann–Liouville type integral nonlinearity, supplemented with a combination of fixed and nonlocal (dual) anti-periodic boundary conditions. The existence results for the given problem are obtained for convex and non-convex cases of the multi-valued map by applying the standard tools of the fixed point theory. Examples illustrating the obtained results are presented.

scholarly journals Fractional Differential Equation Involving Mixed Nonlinearities with Nonlocal Multi-Point and Riemann-Stieltjes Integral-Multi-Strip Conditions

2019 ◽  
Vol 3 (2) ◽  
pp. 34 ◽  
Author(s):  
Ahmad ◽  
Alsaedi ◽  
Salem ◽  
Ntouyas
Keyword(s):  
Fixed Point Theory ◽  
Point Theory ◽  
Stieltjes Integral ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Special Cases ◽  
Mixed Nonlinearities ◽  
Fractional Differential ◽  
The Given

In this paper, we investigate a new class of boundary value problems involving fractionaldifferential equations with mixed nonlinearities, and nonlocal multi-point and Riemann–Stieltjesintegral-multi-strip boundary conditions. Based on the standard tools of the fixed point theory,we obtain some existence and uniqueness results for the problem at hand, which are well illustratedwith the aid of examples. Our results are not only in the given configuration but also yield severalnew results as special cases. Some variants of the given problem are also discussed.

scholarly journals Fractional differential equations with nonlocal (parametric type) anti-periodic boundary conditions

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1207-1214 ◽  
Author(s):  
Ravi Agarwal ◽  
Bashir Ahmad ◽  
Juan Nieto
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Intermediate Point ◽  
Fractional Differential ◽  
Fixed End ◽  
The Given ◽  
Sequential Fractional Differential Equations

In this paper, we introduce a new concept of nonlocal anti-periodic boundary conditions and solve fractional and sequential fractional differential equations supplemented with these conditions. The anti-periodic boundary conditions involve a nonlocal intermediate point together with one of the fixed end points of the interval under consideration, and accounts for a flexible situation concerning anti-periodic phenomena. The existence results for the given problems are obtained with the aid of standard fixed point theorems. Some examples illustrating the main results are also discussed. The paper concludes with several interesting observations.

scholarly journals Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems

2021 ◽  
Vol 2 (1) ◽  
pp. 47-61
Author(s):  
Laila Hashtamand
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Fractional Order Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Stability Results

This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

scholarly journals Existence results for coupled nonlinear fractional differential equations of different orders with nonlocal coupled boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Alsaedi ◽  
Soha Hamdan ◽  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Arbitrary Domain ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractThis paper is concerned with the solvability of coupled nonlinear fractional differential equations of different orders supplemented with nonlocal coupled boundary conditions on an arbitrary domain. The tools of the fixed point theory are applied to obtain the criteria ensuring the existence and uniqueness of solutions of the problem at hand. Examples illustrating the main results are presented.

scholarly journals Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications

2021 ◽  
Vol 41 (4) ◽  
pp. 489-507
Author(s):  
Abdelrachid El Amrouss ◽  
Omar Hammouti
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Critical Point Theory ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Difference Operator ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Existence Of A Solution ◽  
Order Difference

Let \(n\in\mathbb{N}^{*}\), and \(N\geq n\) be an integer. We study the spectrum of discrete linear \(2n\)-th order eigenvalue problems \[\begin{cases}\sum_{k=0}^{n}(-1)^{k}\Delta^{2k}u(t-k) = \lambda u(t) ,\quad & t\in[1, N]_{\mathbb{Z}}, \\ \Delta^{i}u(-(n-1))=\Delta^{i}u(N-(n-1)),\quad & i\in[0, 2n-1]_{\mathbb{Z}},\end{cases}\] where \(\lambda\) is a parameter. As an application of this spectrum result, we show the existence of a solution of discrete nonlinear \(2n\)-th order problems by applying the variational methods and critical point theory.

scholarly journals Existence Results for a Riemann-Liouville-Type Fractional Multivalued Problem with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hamed H. Alsulami ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Multivalued Maps ◽  
Liouville Type ◽  
Integral Boundary ◽  
Fractional Differential ◽  
The Right

We discuss the existence of solutions for a boundary value problem of Riemann-Liouville fractional differential inclusions of orderα∈(2,3]with integral boundary conditions. We establish our results by applying the standard tools of fixed point theory for multivalued maps when the right-hand side of the inclusion has convex as well as nonconvex values. An illustrative example is also presented.

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