scholarly journals Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Erdal Karapınar ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

scholarly journals On the existence and Ulam-Hyers stability of a new class of partial (Φ,χ)-fractional differential equations with impulses

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1977-1991
Author(s):  
Arjumand Seemab ◽  
ur Mujeeb Rehman ◽  
Michal Feckan ◽  
Jehad Alzabut ◽  
Syed Abbas
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Stability Of Solutions ◽  
New Class ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

In this paper, we consider the newly defined partial (?,?)-fractional integral and derivative to study a new class of partial fractional differential equations with impulses. The existence and Ulam-Hyers stability of solutions for the proposed equation are investigated via the means of measure of noncompactness and fixed point theorems. The presented results are quite general in their nature and further complement the existing ones.

Caputo-Hadamard fractional differential equations in banach spaces

2018 ◽  
Vol 21 (4) ◽  
pp. 1027-1045 ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Naima Hamidi ◽  
Johnny Henderson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Hadamard Fractional Differential Equations ◽  
Mönch’S Fixed Point Theorem ◽  
Fractional Differential

Abstract This article deals with some existence results for a class of Caputo–Hadamard fractional differential equations. The results are based on the Mönch’s fixed point theorem associated with the technique of measure of noncompactness. Two illustrative examples are presented.

scholarly journals On the controllability of Hilfer-Katugampola fractional differential equations

2020 ◽  
Vol 24 (2) ◽  
pp. 195-204
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Fractional Differential

By employing Kuratowski's measure of noncompactness together with Sadovskii's fixed point theorem, sufficient conditions for controllability results of Hilfer-Katugampola fractional differential equations in Banach spaces are derived.

scholarly journals On Fuzzy Extended Hexagonal b-Metric Spaces with Applications to Nonlinear Fractional Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2032
Author(s):  
Sumaiya Tasneem Zubair ◽  
Kalpana Gopalan ◽  
Thabet Abdeljawad ◽  
Bahaaeldin Abdalla
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Feasible Solution ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Fractional Differential Equations ◽  
Research Article ◽  
Fractional Differential

The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal b-metric spaces is specified as follows utilizing the function b(c,d): mhc,d,t+s+u+v+w≥mhc,e,tb(c,d)∗mhe,f,sb(c,d)∗mhf,g,ub(c,d)∗mhg,k,vb(c,d)∗mhk,d,wb(c,d) for all t,s,u,v,w>0 and c≠e,e≠f,f≠g,g≠k,k≠d. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained.

Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals

2020 ◽  
Vol 21 (2) ◽  
pp. 135-145 ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Measure Of Noncompactness ◽  
Pettis Integral ◽  
Existence Of Weak Solutions ◽  
Fractional Differential

AbstractIn this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions.

scholarly journals Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

2019 ◽  
Vol 52 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Ulam Stability ◽  
Fractional Differential System ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

scholarly journals Some Existence Results for a System of Nonlinear Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Eskandar Ameer ◽  
Hassen Aydi ◽  
Hüseyin Işık ◽  
Muhammad Nazam ◽  
Vahid Parvaneh ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Cauchy Sequence ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

In this paper, we show that a sequence satisfying a Suzuki-type JS-rational contraction or a generalized Suzuki-type Ćirić JS-contraction, under some conditions, is a Cauchy sequence. This paper presents some common fixed point theorems and an application to resolve a system of nonlinear fractional differential equations. Some examples and consequences are also given.

scholarly journals Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations withp-Laplacian Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Laplacian Operator ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

This paper studies the existence of solutions for a nonlinear boundary value problem of impulsive fractional differential equations withp-Laplacian operator. Our results are based on some standard fixed point theorems. Examples are given to show the applicability of our results.

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