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 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.

Existence of solutions for sequential fractional differential equations with four-point nonlocal fractional integral boundary conditions

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Bashir Ahmad ◽  
Ahmed Alsaedi ◽  
Hana Al-Hutami
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractThis paper investigates the existence of solutions for a nonlinear boundary value problem of sequential fractional differential equations with four-point nonlocal Riemann-Liouville type fractional integral boundary conditions. We apply Banach’s contraction principle and Krasnoselskii’s fixed point theorem to establish the existence of results. Some illustrative examples are also presented.

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 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.

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