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 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.

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.

scholarly journals Existence and Uniqueness Results for Fractional Differential Equations with Riemann-Liouville Fractional Integral Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Uniqueness Result ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

We prove the existence and uniqueness of solution for fractional differential equations with Riemann-Liouville fractional integral boundary conditions. The first existence and uniqueness result is based on Banach’s contraction principle. Moreover, other existence results are also obtained by using the Krasnoselskii fixed point theorem. An example is given to illustrate the main results.

scholarly journals Existence and Uniqueness Results for Hadamard-Type Fractional Differential Equations with Nonlocal Fractional Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Phollakrit Thiramanus ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

We study the existence and uniqueness of solutions for a fractional boundary value problem involving Hadamard-type fractional differential equations and nonlocal fractional integral boundary conditions. Our results are based on some classical fixed point theorems. Some illustrative examples are also included.

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 On a system of Riemann–Liouville fractional differential equations with coupled nonlocal boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Point Theory ◽  
Fractional Integrals ◽  
Fractional Differential

AbstractWe investigate the existence of solutions for a system of Riemann–Liouville fractional differential equations with nonlinearities dependent on fractional integrals, subject to coupled nonlocal boundary conditions which contain various fractional derivatives and Riemann–Stieltjes integrals. In the proof of our main results, we use some theorems from the fixed point theory.

scholarly journals Boundary value problems for Caputo fractional differential equations with nonlocal and fractional integral boundary conditions

2020 ◽  
Vol 9 (3) ◽  
pp. 531-544
Author(s):  
Choukri Derbazi ◽  
Hadda Hammouche
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

Abstract In this paper, we study the existence and uniqueness of solutions for fractional differential equations with nonlocal and fractional integral boundary conditions. New existence and uniqueness results are established using the Banach contraction principle. Other existence results are obtained using O’Regan fixed point theorem and Burton and Kirk fixed point. In addition, an example is given to demonstrate the application of our main results.

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