scholarly journals Random Coupled Hilfer and Hadamard Fractional Differential Systems in Generalized Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 285 ◽  
Author(s):  
Saïd Abbas ◽  
Nassir Arifi ◽  
Mouffak Benchohra ◽  
Yong Zhou
Keyword(s):  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Uniqueness Result ◽  
Coupled Systems ◽  
Random Fixed Point ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

This article deals with some existence and uniqueness result of random solutions for some coupled systems of Hilfer and Hilfer–Hadamard fractional differential equations with random effects. Some applications are made of generalizations of classical random fixed point theorems on generalized Banach spaces.

scholarly journals Existence-uniqueness of positive solutions to nonlinear impulsive fractional differential systems and optimal control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu Song ◽  
Lingling Zhang ◽  
Bibo Zhou ◽  
Nan Zhang
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Mixed Monotone Operator ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential

Abstract In this thesis, we investigate a kind of impulsive fractional order differential systems involving control terms. By using a class of φ-concave-convex mixed monotone operator fixed point theorem, we obtain a theorem on the existence and uniqueness of positive solutions for the impulsive fractional differential equation, and the optimal control problem of positive solutions is also studied. As applications, an example is offered to illustrate our main results.

scholarly journals Separated Boundary Value Problems of Sequential Caputo and Hadamard Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jessada Tariboon ◽  
Asawathep Cuntavepanit ◽  
Sotiris K. Ntouyas ◽  
Woraphak Nithiarayaphaks
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this paper, we discuss the existence and uniqueness of solutions for new classes of separated boundary value problems of Caputo-Hadamard and Hadamard-Caputo sequential fractional differential equations by using standard fixed point theorems. We demonstrate the application of the obtained results with the aid of examples.

scholarly journals Existence and Uniqueness for a System of Caputo-Hadamard Fractional Differential Equations with Multipoint Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
S. Nageswara Rao ◽  
Ahmed Hussein Msmali ◽  
Manoj Singh ◽  
Abdullah Ali H. Ahmadini
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

In this paper, we study existence and uniqueness of solutions for a system of Caputo-Hadamard fractional differential equations supplemented with multi-point boundary conditions. Our results are based on some classical fixed point theorems such as Banach contraction mapping principle, Leray-Schauder fixed point theorems. At last, we have presented two examples for the illustration of main results.

Solvability of Anti-periodic BVPs for Impulsive Fractional Differential Systems Involving Caputo and Riemann–Liouville Fractional Derivatives

2018 ◽  
Vol 19 (2) ◽  
pp. 125-152 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Fixed Point ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Conclusion Section

AbstractSufficient conditions are given for the existence of solutions of anti-periodic value problems for impulsive fractional differential systems involving both Caputo and Riemann–Liouville fractional derivatives. We allow the nonlinearities$p(t)f(t,x,y,z,w)$and$q(t)g(t,x,y,z,w)$in fractional differential equations to be singular at$t=0$and$t=1$. Both$f$and$g$may be super-linear and sub-linear. The analysis relies on some well known fixed point theorems. The initial value problem discussed may be seen as a generalization of some ecological models. An example is given to illustrate the efficiency of the main theorems. Many unsuitable lemmas in recent published papers are pointed out in order not to mislead readers. A conclusion section is given at the end of the paper.

scholarly journals Existence of Positive Solution for Fractional Differential Systems with Multipoint Boundary Value Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhi-Wei Lv
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Differential Systems ◽  
Multipoint Boundary ◽  
Fractional Differential Systems ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Convex Operators

In this paper, we apply the fixed-point theorems of γ concave and −γ convex operators to establish the existence of positive solutions for fractional differential systems with multipoint boundary conditions. Two examples are given to support our results.

scholarly journals Existence and uniqueness of positive solutions for nonlinear Caputo-Hadamard fractional differential equations

2021 ◽  
Vol 40 (1) ◽  
pp. 139-152
Author(s):  
Abdelouaheb Ardjouni
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solution ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

We prove the existence and uniqueness of a positive solution of nonlinear Caputo-Hadamard fractional differential equations. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.

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