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Your search keyword '"Existence theory"' showing total 12 results
Start Over Descriptor "Existence theory" Journal advances in difference equations
12 results on '"Existence theory"'

1. Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative

Author

Manar A. Alqudah, Thabet Abdeljawad, Eiman, Kamal Shah, Fahd Jarad, and Qasem Al-Mdallal

Subjects
Prey–predator system, Existence theory, Laplace transform coupled with Adomian method, Mathematics, QA1-939
Abstract

Abstract This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent example of prey–predator system, we support our results. Some graphical presentations are given using Matlab.

Published
2020
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2. Study of implicit delay fractional differential equations under anti-periodic boundary conditions

Author

Arshad Ali, Kamal Shah, and Thabet Abdeljawad

Subjects
Pantograph differential equation, Existence theory, Hyers–Ulam stability, Mathematics, QA1-939
Abstract

Abstract This research work is related to studying a class of special type delay implicit fractional order differential equations under anti-periodic boundary conditions. With the help of classical fixed point theory due to Schauder and Banach, we derive some results about the existence of at least one solution. Further, we also study some results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam Rassias, and generalized Hyers–Ulam–Rassias stability. We provide some test problems for illustrating our analysis.

Published
2020
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3. Analysis of coupled systems of implicit impulsive fractional differential equations involving Hadamard derivatives

Author

Usman Riaz, Akbar Zada, Zeeshan Ali, Yujun Cui, and Jiafa Xu

Subjects
Hadamard fractional derivative, Nonlinear implicit impulsive coupled system, Existence theory, Hyers–Ulam stability, Mathematics, QA1-939
Abstract

Abstract We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative. Using a fixed point theorem of Kransnoselskii’s type, the existence and uniqueness results are obtained. Along these lines, different kinds of Hyers–Ulam stability are discussed. An example is given to illustrate the main theorems.

Published
2019
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4. Note on the solution of random differential equations via ψ-Hilfer fractional derivative

Author

S. Harikrishnan, Kamal Shah, Dumitru Baleanu, and K. Kanagarajan

Subjects
Random differential equations, ψ-Hilfer fractional derivative, Existence theory, Stability analysis, Mathematics, QA1-939
Abstract

Abstract This manuscript is devoted to an investigation of the existence, uniqueness and stability of random differential equations with ψ-Hilfer fractional derivative. The concerned investigation of existence and uniqueness is obtained via the Schauder fixed point theorem and Banach contraction principle, respectively. Furthermore, for the respective solutions, some results related to different kinds of Ulam type stability including Hyers–Ulam, and generalized Hyers–Ulam, Hyers–Ulam–Rassias are obtained.

Published
2018
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5. Study of implicit delay fractional differential equations under anti-periodic boundary conditions.

Author

Ali, Arshad, Shah, Kamal, and Abdeljawad, Thabet

Subjects
*FIXED point theory, *FRACTIONAL differential equations, *DELAY differential equations, *DIFFERENTIAL equations
Abstract

This research work is related to studying a class of special type delay implicit fractional order differential equations under anti-periodic boundary conditions. With the help of classical fixed point theory due to Schauder and Banach, we derive some results about the existence of at least one solution. Further, we also study some results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam Rassias, and generalized Hyers–Ulam–Rassias stability. We provide some test problems for illustrating our analysis. [ABSTRACT FROM AUTHOR]

Published
2020
Full Text
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6. Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative

Author

Fahd Jarad, Manar A. Alqudah, Kamal Shah, Qasem M. Al-Mdallal, Thabet Abdeljawad, and Eiman

Subjects
Existence theory, Algebra and Number Theory, Partial differential equation, Laplace transform, Applied Mathematics, lcsh:Mathematics, Fixed point, Type (model theory), lcsh:QA1-939, 01 natural sciences, 010305 fluids & plasmas, law.invention, Nonlinear system, Invertible matrix, law, Ordinary differential equation, Kernel (statistics), 0103 physical sciences, Prey–predator system, Laplace transform coupled with Adomian method, Applied mathematics, 010306 general physics, Analysis, Mathematics
Abstract

This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent example of prey–predator system, we support our results. Some graphical presentations are given using Matlab.

Published
2020
Full Text
View/download PDF

8. Study of implicit delay fractional differential equations under anti-periodic boundary conditions

Author

Thabet Abdeljawad, Kamal Shah, and Arshad Ali

Subjects
Existence theory, Hyers–Ulam stability, Mathematics::Functional Analysis, Algebra and Number Theory, Partial differential equation, Mathematics::Operator Algebras, Differential equation, lcsh:Mathematics, Applied Mathematics, Mathematics::Classical Analysis and ODEs, Fixed-point theorem, Pantograph differential equation, Type (model theory), lcsh:QA1-939, Stability (probability), Ordinary differential equation, Applied mathematics, Periodic boundary conditions, Boundary value problem, Analysis, Mathematics
Abstract

This research work is related to studying a class of special type delay implicit fractional order differential equations under anti-periodic boundary conditions. With the help of classical fixed point theory due to Schauder and Banach, we derive some results about the existence of at least one solution. Further, we also study some results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam Rassias, and generalized Hyers–Ulam–Rassias stability. We provide some test problems for illustrating our analysis.

Published
2020
Full Text
View/download PDF

9. Note on the solution of random differential equations via ψ-Hilfer fractional derivative

Author

Kamal Shah, S. Harikrishnan, Dumitru Baleanu, and Kuppusamy Kanagarajan

Subjects
Differential equation, Type (model theory), 01 natural sciences, Schauder fixed point theorem, Uniqueness, 0101 mathematics, Nonlinear Sciences::Pattern Formation and Solitons, ψ-Hilfer fractional derivative, Mathematics, Existence theory, Mathematics::Functional Analysis, Algebra and Number Theory, Partial differential equation, Mathematics::Operator Algebras, Applied Mathematics, lcsh:Mathematics, 010102 general mathematics, Mathematical analysis, Stability analysis, lcsh:QA1-939, Fractional calculus, Nonlinear Sciences::Chaotic Dynamics, 010101 applied mathematics, Random differential equations, Ordinary differential equation, Contraction principle, Analysis
Abstract

This manuscript is devoted to an investigation of the existence, uniqueness and stability of random differential equations with ψ-Hilfer fractional derivative. The concerned investigation of existence and uniqueness is obtained via the Schauder fixed point theorem and Banach contraction principle, respectively. Furthermore, for the respective solutions, some results related to different kinds of Ulam type stability including Hyers–Ulam, and generalized Hyers–Ulam, Hyers–Ulam–Rassias are obtained.

Published
2018
Full Text
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11. Analysis of coupled systems of implicit impulsive fractional differential equations involving Hadamard derivatives

Author

Yujun Cui, Jiafa Xu, Akbar Zada, Zeeshan Ali, and Usman Riaz

Subjects
Existence theory, Hyers–Ulam stability, Mathematics::Functional Analysis, Algebra and Number Theory, Partial differential equation, lcsh:Mathematics, Applied Mathematics, Nonlinear implicit impulsive coupled system, Fixed-point theorem, Type (model theory), lcsh:QA1-939, Stability (probability), Fractional calculus, Hadamard transform, Ordinary differential equation, Hadamard fractional derivative, Applied mathematics, Uniqueness, Analysis, Mathematics
Abstract

We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative. Using a fixed point theorem of Kransnoselskii’s type, the existence and uniqueness results are obtained. Along these lines, different kinds of Hyers–Ulam stability are discussed. An example is given to illustrate the main theorems.

Published
2019
Full Text
View/download PDF

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