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  1. 33 Demonstratio Mathematica
  2. 9 Journal of Mathematics and Applications
  3. 8 Journal of Applied Analysis
  4. 3 Journal of Applied Mathematics and Computational Mechanics
  5. 1 Annales Societatis Mathematicae Polonae. Series 3: Mathematica Applicanda
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  1. 2 Djoudi A.
  2. 2 EL-Fassi I.
  3. 2 Klamka J.
  4. 2 O'Regan D.
  5. 2 Shah Vishant
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  1. 1 2024
  2. 1 2023
  3. 1 2022
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  5. 5 2020
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1
Content available On the stability analysis for a semi-analytical scheme for solving the fractional order blood ethanol concentration system using LVIM
Adel Mohamed, Sweilam Nasser H., Khader Mohamed M.
Journal of Applied Mathematics and Computational Mechanics
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2024
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Vol. 23, nr 1
7-18
EN
The purpose of this article is to present the Laplace variational iteration method, which combines the VIM with the Laplace transform approach (LVIM). This combination will result in a better and more quickly convergent sequence since nonlinear fractional differential equations (FDEs) cannot be solved using the Laplace transform. With the use of the fixed point theory, the stability analysis is specifically discussed and examined. The blood ethanol concentration system is solved numerically by using the suggested scheme. This model can be represented by a system of FDEs. The investigation will emploi the Caputo-Fabrizio fractional derivative. To provide a more in-depth study of this model, we have taken it in its fractional form so that we can more accurately follow the behavior of the solution in the future and history based on the memory effect of fractional derivatives. We determine the accuracy and efficiency of the provided process by evaluating the absolute errors, and a comparison with the existing published work. The results show that the approach is a useful tool for simulating this model.
2
Content available On solution of non-instantaneous impulsive Hilfer fractional integro-differential evolution system
Trivedi Gargi J., Shah Vishant, Sharma Jaita, Sanghvi Rajesh
Mathematica Applicanda
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2023
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Vol. 51, no. 1
33--50
EN
In this article, we have considered the non-instantaneous fractional integrodifferential evolution system with Hilfer fractional differential operator in the Banach space and discussed its existence results for the mild solution for the equation with local and non-local conditions. These results are obtained by applying the method of a C0 operator generated by the linear part of the equation combined with the concept of nonlinear functional analysis and the fixed point theorems. We have discussed the examples to highlight the applicability of the results.
PL
Artykuł poświęcony jest ułamkowym, z opóźnieniem, systemom ewolucji całkowo-różniczkowej opisanym ułamkowym operatorem różniczkowym Hilfera w przestrzeni Banacha. Analizowane jest istnienia gładkiego rozwiązania równania z warunkami lokalnymi i nielokalnymi. Wyniki uzyskano stosując do operatora C0 generowanego przez liniową część równania metody nieliniowej analizy funkcjonalnej z twierdzeniami o punkcie stałym. Zamieszczone przykłady podkreślają znaczenie otrzymanych wyników.
3
Content available remote Generalized common fixed point theorem for generalized hybrid mappings in Hilbert spaces
Kondo Atsumasa
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
752--759
EN
In this article, we prove a common fixed point theorem for commutative nonlinear mappings that jointly satisfy a certain condition. From the main theorem, a common fixed point theorem for commutative generalized hybrid mappings is derived as a special case. Our novel approach significantly expands the applicable range of mappings for well-known fixed point theorems to be effective. Examples are presented to explicitly illustrate this contribution.
4
Content available remote On some fixed point theorems for multivalued F-contractions in partial metric spaces
Kumar Santosh, Luambano Sholastica
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
151--161
EN
Altun et al. explored the existence of fixed points for multivalued F-contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F-contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.
5
Content available On the existence of continuous positive monotonic solutions of a self-reference quadratic integral equation
El-Sayed Ahmed M.A., Ebead Hanaa R.
Journal of Mathematics and Applications
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2020
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Vol. 43
67--80
EN
In this work we study the existence of positive monotonic solutions of a self-reference quadratic integral equation in the class of continuous real valued functions. The continuous dependence of the uniquesolution will be proved. Some examples will be given.
6
Content available Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with ψ-Caputo fractional derivative
Wahash Hanan A., Abdo Mohammed S, Panchal Satish K.
Journal of Applied Mathematics and Computational Mechanics
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2020
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Vol. 19, nr 1
89--101
EN
In this paper, we investigate the existence, uniqueness and Ulam-Hyers stability of solutions for nonlinear implicit fractional differential equations with boundary conditions involving a ψ-Caputo fractional derivative. The obtained results for the proposed problem are proved under a new approach and minimal assumptions on the function ƒ. The analysis is based upon the reduction of the problem considered to the equivalent integral equation, while some fixed point theorems of Banach and Schauder and generalized Gronwall inequality are employed to obtain our results for the problem at hand. Finally, the investigation is illustrated by providing a suitable example.
7
Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
Hellal Meryem, Merzagui N.
Journal of Applied Analysis
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2020
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Vol. 26, nr 2
193--207
EN
In this work, we use the fixed-point theorem in double cones to study the existence of multiple positive solutions for an impulsive first-order differential system with integral boundary conditions, when the nonlinearities change sign.
8
Content available remote Stability of an additive-quadratic-quartic functional equation
Kim Gwang Hui, Lee Yang-Hi
Demonstratio Mathematica
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2020
|
Vol. 53, nr 1
1--7
EN
In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x-2y) - 2f(x+y) - 2f(-x-y) - 2f(x-y) - 2f(y-x)+4f(-x)+2f(x) - f(2y) - f(-2y)+4f(y)+4f(-y)=0 by the direct method in the sense of Găvruta.
9
Content available remote Existence results of noninstantaneous impulsive fractional integro-differential equation
Kataria Haribhai R., Patel Prakashkumar H., Shah Vishant
Demonstratio Mathematica
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2020
|
Vol. 53, nr 1
373--384
EN
Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.
10
Content available The existence of monotonic solutions of a class of quadratic integral equations of Volterra type
Karakurt Osman, Temizer Ӧmer Faruk
Journal of Mathematics and Applications
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2019
|
Vol. 42
117--133
EN
Using the technique associated with measure of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.
11
Content available Nonincreasing solutions for quadratic integral equations of Convolution type
El-Sayed W. G., Abd El-Mowla A. A. H.
Journal of Mathematics and Applications
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2019
|
Vol. 42
95--107
EN
We study a nonlinear quadratic integral equation of Convolution type in the Banach space of real functions defined and continuous on a bounded and closed interval. By using a suitable measure of noncompactness, we show that the integral equation has monotonic solutions.
12
Content available Fixed point theorems for monotone mappings in ordered Banach spaces under weak topology features
Alahmari Abdullah, Mabrouk Mohamed, Taoudi Mohamed-Aziz
Journal of Mathematics and Applications
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2019
|
Vol. 42
5--19
EN
We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vectorvalued ordinary differential equations. Our conclusions generalize many well-known results.
13
Content available Existence and uniqueness of solutions for nonlinear Katugampola fractional differential equations
Basti Bilal, Arioua Yacine, Benhamidouche Nouredine
Journal of Mathematics and Applications
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2019
|
Vol. 42
35--61
EN
The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach fixed point theorems. For applications purposes, some examples are provided to demonstrate the usefulness of our main results.
14
Content available remote Hyers-Ulam stability of a coupled system of fractional differential equations of Hilfer-Hadamard type
Ahmad Manzoor, Zada Akbar, Alzabut Jehad
Demonstratio Mathematica
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2019
|
Vol. 52, nr 1
283--295
EN
In 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.
15
Content available remote Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative
Benchohra Mouffak, Bouriah Soufyane, Nieto Juan J.
Demonstratio Mathematica
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2019
|
Vol. 52, nr 1
437--450
EN
In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.
16
Content available remote Convergence and stability of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping
Aggarwal Sajan, Uddin Izhar
Demonstratio Mathematica
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2019
|
Vol. 52, nr 1
388--396
EN
In this paper, we prove strong convergence and ∆-convergence of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping (i.e. nearly asymptotically nonexpansive mapping) in partially ordered hyperbolic metric space. Moreover, we prove stability of Fibonacci-Mann iteration. Further, we construct a numerical example to illustrate results. Our results simultaneously generalize the results of Alfuraidan and Khamsi [Bull. Aust. Math. Soc., 2017, 96, 307-316] and Schu [J. Math. Anal. Appl., 1991, 58, 407-413].
17
Content available Positive solution of a fractional differential equation with integral boundary conditions
Abdo M. S., Wahash H. A., Panchal S. K.
Journal of Applied Mathematics and Computational Mechanics
|
2018
|
Vol. 17, nr 3
5--15
EN
In this paper, we prove the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional differential equations involving a Caputo fractional operator with integral boundary conditions. The technique used to prove our results depends on the upper and lower solution, the Schauder fixed point theorem and the Banach contraction principle. The result of existence obtained through constructing the upper and lower control functions of the nonlinear term without any monotone requirement.
18
Non-Archimedean hyperstability of Cauchy-Jensen functional equations on a restricted domain
EL-Fassi I.
Journal of Applied Analysis
|
2018
|
Vol. 24, nr 2
155--165
EN
Let X be a normed space, U ⊂ X \ {0} a non-empty subset, and (G, +) a commutative group equipped with a complete ultrametric d that is invariant (i.e., d(x + z, y + z) = d(x, y) for x, y, z ∈ G). Under some weak natural assumptions on U and on the function γ : U3 → [0, ∞), we study the new generalized hyperstability results when f : U → G satisfies the inequality d(αf( x + y / α + z), αf(z) + f(y) + f(x)) ≤ γ(x, y, z) for all x, y, z ∈ U, where x+y α + z ∈ U and α ≥ 2 is a fixed positive integer. The method is based on a quite recent fixed point theorem (Theorem 1 in [J. Brzdęk and K. Ciepliński, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Anal. 74 (2011), no. 18, 6861-6867]) in some functions spaces.
19
Content available remote Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces
EL-Fassi I., Park C., Kim G. H.
Demonstratio Mathematica
|
2018
|
Vol. 51, nr 1
295--303
EN
We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.
20
Content available On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order
Metwali M. M. A.
Journal of Mathematics and Applications
|
2017
|
Vol. 40
121--p134
EN
The paper discusses the existence of solutions for Cauchy-type problem of fractional order in the space of Lebesgue integrable functions on bounded interval. Some qualitative properties of solutions are presented such as monotonicity, uniqueness and continuous dependence on the initial data. The main tools used are measure of weak (strong) noncompactness, Darbo fixed point theorem and fractional calculus.
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