Existence theorems for semi-linear Caputo fractional differential equations with nonlocal discrete and integral boundary conditions

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
Doa’a Qarout ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Existence Theorems ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

AbstractIn this paper, we introduce and study a new class of boundary value problems of one-dimensional higher-order semi-linear Caputo type fractional differential equations and nonlocal multi-point discrete and integral boundary conditions. Our existence results are new in the given setting and rest on some standard tools of fixed point theory. We also discuss Riemann-Liouville and Stieltjes variants of the proposed problem. The obtained results are well illustrated with the aid of examples.

Caputo type fractional differential equations with nonlocal Riemann-Liouville and Erdélyi-Kober type integral boundary conditions

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4515-4529 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas ◽  
Jessada Tariboon ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we study nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with different combinations of Riemann-Liouville and Erd?lyi-Kober type fractional integral boundary conditions. By applying a variety of tools of fixed point theory, the desired existence and uniqueness results are obtained. Examples illustrating the main results are also constructed.

scholarly journals Study of a Class of Generalized Multiterm Fractional Differential Equations with Generalized Fractional Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Wafa Shammakh ◽  
Hadeel Z. Alzumi ◽  
Zahra Albarqi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

The aim of this work is to study the new generalized fractional differential equations involving generalized multiterms and equipped with multipoint boundary conditions. The nonlinear term is taken from Orlicz space. The existence and uniqueness results, with the help of contemporary tools of fixed point theory, are investigated. The Ulam stability of our problem is also presented. The obtained results are well illustrated by examples.

scholarly journals Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions

2016 ◽  
Vol 14 (1) ◽  
pp. 723-735 ◽  
Author(s):  
Mohammed H. Aqlan ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Existence Theory ◽  
Integral Boundary ◽  
Special Cases ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractWe develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.

scholarly journals New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Haiyan Zhang ◽  
Yaohong Li ◽  
Jingbao Yang
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Mixed Type ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Type Boundary ◽  
Sequential Fractional Differential Equations

In this paper, we introduce new sequential fractional differential equations with mixed-type boundary conditions CDq+kCDq−1ut=ft,ut,CDq−1ut,t∈0,1,α1u0+β1u1+γ1Iruη=ε1,η∈0,1,α2u′0+β2u′1+γ2Iru′η=ε2, where q∈1,2 is a real number, k,r>0,αi,βi,γi,εi∈ℝ,i=1,2,CDq is the Caputo fractional derivative, and the boundary conditions include antiperiodic and Riemann-Liouville fractional integral boundary value cases. Our approach to treat the above problem is based upon standard tools of fixed point theory and some new inequalities of norm form. Some existence results are obtained and well illustrated through the aid of examples.

scholarly journals On coupled Hadamard type sequential fractional differential equations with variable coefficients and nonlocal integral boundary conditions

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6041-6049 ◽  
Author(s):  
Shorog Aljoudi ◽  
Bashir Ahmad ◽  
Juan Nieto ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Variable Coefficients ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Nonlocal Integral Boundary Conditions ◽  
Sequential Fractional Differential Equations

In this paper, we develop the existence criteria for the solutions of a system of Hadamard type sequential fractional differential equations with variable coefficients and nonlocal integral boundary conditions. The main results rely on the standard tools of fixed-point theory. An illustrative example is also discussed.

scholarly journals Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions

2018 ◽  
Vol 17 (1) ◽  
pp. 103-125 ◽  
Author(s):  
Akbar Zada ◽  
Mohammad Yar ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Caputo Fractional Differential Equations ◽  
Existence And Stability ◽  
Fractional Differential

Abstract In this paper we study existence and uniqueness of solutions for a coupled system consisting of fractional differential equations of Caputo type, subject to Riemann–Liouville fractional integral boundary conditions. The uniqueness of solutions is established by Banach contraction principle, while the existence of solutions is derived by Leray–Schauder’s alternative. We also study the Hyers–Ulam stability of mentioned system. At the end, examples are also presented which illustrate our results.

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