scholarly journals Existence Results for a System of Coupled Hybrid Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Result ◽  
Existence Results ◽  
Dirichlet Boundary Conditions ◽  
Fractional Differential

This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations with Dirichlet boundary conditions. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.

scholarly journals Qualitative Analysis of Implicit Dirichlet Boundary Value Problem for Caputo-Fabrizio Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Rozi Gul ◽  
Muhammad Sarwar ◽  
Kamal Shah ◽  
Thabet Abdeljawad ◽  
Fahd Jarad
Keyword(s):  
Differential Equations ◽  
Qualitative Analysis ◽  
Fractional Differential Equations ◽  
Dirichlet Boundary ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Dirichlet Boundary Conditions ◽  
Fractional Differential ◽  
The Stability ◽  
Implicit Fractional Differential Equations

This article studies a class of implicit fractional differential equations involving a Caputo-Fabrizio fractional derivative under Dirichlet boundary conditions (DBCs). Using classical fixed-point theory techniques due to Banch’s and Krasnoselskii, a qualitative analysis of the concerned problem for the existence of solutions is established. Furthermore, some results about the stability of the Ulam type are also studied for the proposed problem. Some pertinent examples are given to justify the results.

scholarly journals Existence Results for a System of Coupled Hybrid Differential Equations with Fractional Order

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Mohamed Hannabou ◽  
Khalid Hilal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Result ◽  
Existence Results ◽  
Fractional Differential ◽  
Hybrid Differential Equations

This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.

scholarly journals On Antiperiodic Boundary Value Problems for Higher-Order Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Afrah Assolami
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

We study an antiperiodic boundary value problem of nonlinear fractional differential equations of orderq∈(4,5]. Some existence results are obtained by applying some standard tools of fixed-point theory. We show that solutions for lower-order anti-periodic fractional boundary value problems follow from the solution of the problem at hand. Our results are new and generalize the existing results on anti-periodic fractional boundary value problems. The paper concludes with some illustrating examples.

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.

Coupled fractional differential systems with random effects in Banach spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
O. Zentar ◽  
M. Ziane ◽  
S. Khelifa
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Random Differential Equations ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Vector Valued ◽  
Abstract Formulation

Abstract The purpose of this work is to investigate the existence of solutions for a system of random differential equations involving the Riemann–Liouville fractional derivative. The existence result is established by means of a random abstract formulation to Sadovskii’s fixed point theorem principle [A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory Appl. 2017 2017, Paper No. 27] combined with a technique based on vector-valued metrics and convergent to zero matrices. An example is also provided to illustrate our result.

scholarly journals Existence and uniqueness results for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4881-4891
Author(s):  
Adel Lachouri ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we use the fixed point theory to obtain the existence and uniqueness of solutions for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions. An example is given to illustrate this work.

scholarly journals A note regarding extensions of fixed point theorems involving two metrics via an analysis of iterated functions

2020 ◽  
Vol 61 ◽  
pp. C15-C30
Author(s):  
Charles P Stinson ◽  
Saleh S Almuthaybiri ◽  
Christopher C Tisdell
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Nonlinear Dynamic Equations ◽  
Fractional Differential

The purpose of this work is to advance the current state of mathematical knowledge regarding fixed point theorems of functions. Such ideas have historically enjoyed many applications, for example, to the qualitative and quantitative understanding of differential, difference and integral equations. Herein, we extend an established result due to Rus [Studia Univ. Babes-Bolyai Math., 22, 1977, 40–42] that involves two metrics to ensure wider classes of functions admit a unique fixed point. In contrast to the literature, a key strategy herein involves placing assumptions on the iterations of the function under consideration, rather than on the function itself. In taking this approach we form new advances in fixed point theory under two metrics and establish interesting connections between previously distinct theorems, including those of Rus [Studia Univ. Babes-Bolyai Math., 22, 1977, 40–42], Caccioppoli [Rend. Acad. Naz. Linzei. 11, 1930, 31–49] and Bryant [Am. Math. Month. 75, 1968, 399–400]. Our results make progress towards a fuller theory of fixed points of functions under two metrics. Our work lays the foundations for others to potentially explore applications of our new results to form existence and uniqueness of solutions to boundary value problems, integral equations and initial value problems. References Almuthaybiri, S. S. and C. C. Tisdell. ``Global existence theory for fractional differential equations: New advances via continuation methods for contractive maps''. Analysis, 39(4):117–128, 2019. doi:10.1515/anly-2019-0027 Almuthaybiri, S. S. and C. C. Tisdell. ``Sharper existence and uniqueness results for solutions to third-order boundary value problems, mathematical modelling and analysis''. Math. Model. Anal. 25(3):409–420, 2020. doi:10.3846/mma.2020.11043 Banach, S. ``Sur les operations dans les ensembles abstraits et leur application aux equations integrales''. Fund. Math., 3:133–181 1922. doi:10.4064/fm-3-1-133-181 Brouwer, L. E. J. ``Ueber Abbildungen von Mannigfaltigkeiten''. Math. Ann. 71:598, 1912. doi:10.1007/BF01456812 Bryant, V. W. ``A remark on a fixed point theorem for iterated mappings'' Am. Math. Month. 75: 399–400, 1968. doi:10.2307/2313440 Caccioppoli, R. ``Un teorema generale sullesistenza de elemente uniti in una transformazione funzionale''. Rend. Acad. Naz. Linzei. 11:31–49, 1930. Goebel, K., and W. A. Kirk. Topics in metric fixed point theory. Cambridge University Press, 1990, doi:10.1017/CBO9780511526152 Leray, J., and J. Schauder. ``Topologie et equations fonctionnelles''. Ann. Sci. Ecole Norm. Sup. 51:45–78, 1934. doi:10.24033/asens.836 O'Regan, D. and R. Precup. Theorems of Leray–Schauder type and applications, Series in Mathematical Analysis and Applications, Vol. 3. CRC Press, London, 2002. doi:10.1201/9781420022209 Rus, I. A. ``On a fixed point theorem of Maia''. Studia Univ. Babes-Bolyai Math. 22:40–42, 1977. Schaefer, H. H. ``Ueber die Methode der a priori-Schranken''. Math. Ann. 129:415–416, 1955. doi:10.1007/bf01362380 Tisdell, C. C. ``When do fractional differential equations have solutions that are bounded by the Mittag-Leffler function?'' Fract. Calc. Appl. Anal. 18(3):642–650, 2015. doi:10.1515/fca-2015-0039 Tisdell, C. C. ``A note on improved contraction methods for discrete boundary value problems.'' J. Diff. Eq. Appl. 18(10):1773–1777, 2012. doi:10.1080/10236198.2012.681781 Tisdell, C. C. ``On the application of sequential and fixed-point methods to fractional differential equations of arbitrary order.'' J. Int. Eq. Appl. 24(2):283–319, 2012. doi:10.1216/JIE-2012-24-2-283 Ehrnstrom, M., Tisdell, C. C. and E. Wahlen. ``Asymptotic integration of second-order nonlinear difference equations.'' Glasg. Math. J. 53(2):223–243, 2011. doi:10.1017/S0017089510000650 Erbe, L., A. Peterson and C. C. Tisdell. ``Basic existence, uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales.'' Nonlin. Anal. 69(7):2303–2317, 2008. doi:10.1016/j.na.2007.08.010 Tisdell, C. C. and A. Zaidi. ``Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling.'' Nonlin. Anal. 68(11):3504–3524, 2008. doi:10.1016/j.na.2007.03.043 Tisdell, C. C. ``Improved pedagogy for linear differential equations by reconsidering how we measure the size of solutions.'' Int.. J. Math. Ed. Sci. Tech. 48(7):1087–1095, 2017. doi:10.1080/0020739X.2017.1298856 Tisdell, C. C. ``On Picard's iteration method to solve differential equations and a pedagogical space for otherness.'' Int. J. Math. Ed. Sci. Tech. 50(5):788–799, 2019. doi:10.1080/0020739X.2018.1507051 Zeidler, E. Nonlinear functional analysis and its applications. Springer-Verlag, New York, 1986. doi:10.1007/978-1-4612-4838-5

Existence Results to Some Damped-Like Fractional Differential Equations

2017 ◽  
Vol 18 (3-4) ◽  
pp. 233-243 ◽  
Author(s):  
Nemat Nyamoradi ◽  
Yong Zhou
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Existence Of Weak Solutions ◽  
Fractional Differential ◽  
New Criteria ◽  
Fractional Boundary Value Problems

Abstract:In this paper, by using critical point theory and variational methods, we prove the existence of weak solutions for damped-like fractional differential equations. We given some new criteria to distinguish that the fractional boundary value problems have at least one solution. Some examples are also given to illustrate the main results.

scholarly journals The Existence Results of Solutions for System of Fractional Differential Equations with Integral Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Dongxia Zan ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Initial Point ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, we investigated the system of fractional differential equations with integral boundary conditions. By using a fixed point theorem in the Banach spaces, we get the existence of solutions for the fractional differential system. By constructing iterative sequences for any given initial point in space, we can approximate this solution. As an application, an example is presented to illustrate our main results.

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