On solution of non-linear FDE under tempered Ψ−Caputo derivative for the first-order and three-point boundary conditions by K. Bensassa, M. Benbachir, M.E. Samei, S. Salahshour

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Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method by Ali Khalid K., Mohamed Mohamed S., Alharbi Weam G., Maneea Marwa

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Results on non local impulsive implicit Caputo-Hadamard fractional differential equations by K. Venkatachalam, M. Sathish Kumar, P. Jayakumar

“…The results for a new modeling integral boundary value problem using Caputo-Hadamard impulsive implicit fractional differential equations with Banach space are investigated, along with the existence and uniqueness of solutions. The Krasnoselskii fixed-point theorem, Schaefer's fixed point theorem and the Banach contraction principle serve as the basis of this unique strategy, and are used to achieve the desired results. …”
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Solving fractional integro-differential equations with delay and relaxation impulsive terms by fixed point techniques by Doha A. Kattan, Hasanen A. Hammad

“…The system is transformed into an equivalent integral equation, facilitating the application of Banach and Schaefer fixed-point theorems to prove the existence and uniqueness of solutions. …”
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Fixed Point and Stability Analysis of a Tripled System of Nonlinear Fractional Differential Equations with <i>n</i>-Nonlinear Terms by Mohamed S. Algolam, Osman Osman, Arshad Ali, Alaa Mustafa, Khaled Aldwoah, Amer Alsulami

“…The study explores this novel class of differential equations to establish existence and stability results. Utilizing Schaefer’s and Banach’s fixed point theorems, we derive sufficient conditions for the existence of at least one solution, as well as a unique solution. …”
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Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions by Mısır J. Mardanov, Yagub A. Sharifov, Kamala E. Ismayilova

“…Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. …”
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Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. …”
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Fractional Differential Equations with Fractional Impulsive and Nonseparated Boundary Conditions by Xi Fu, Xiaoyou Liu

“…This paper studies the existence results for nonseparated boundary value problems of fractional differential equations with fractional impulsive conditions. By means of Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. …”
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Existence Results for Fractional Differential Equations with Separated Boundary Conditions and Fractional Impulsive Conditions by Xi Fu, Xiaoyou Liu

“…This paper is concerned with the fractional separated boundary value problem of fractional differential equations with fractional impulsive conditions. By means of the Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. …”
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An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space by Asma Bouzaroura, Saïd Mazouzi

“…The derived results are based on Banach's contraction theorem as well as Schaefer's fixed point theorem.…”
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Existence Results for Nonlinear Multiorder Fractional Differential Equations with Integral and Antiperiodic Boundary Conditions by HuiChol Choi, YongSim Sin, KumSong Jong

“…In this paper, we study the solvability of a class of nonlinear multiorder Caputo fractional differential equations with integral and antiperiodic boundary conditions. By using some fixed point theorems including the Banach contraction mapping principle and Schaefer’s fixed point theorem, we obtain new existence and uniqueness results for our given problem. …”
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Solvability of Some Boundary Value Problems for Fractional -Laplacian Equation by Taiyong Chen, Wenbin Liu

“…Under certain nonlinear growth conditions of the nonlinearity, two new existence results are obtained by using Schaefer's fixed point theorem. As an application, an example to illustrate our results is given.…”
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A Nonlinear Implicit Fractional Equation with Caputo Derivative by Ameth Ndiaye

“…Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. At the end, we discuss two examples to illustrate the applicability of the main results.…”
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Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative by Ameth Ndiaye, Fulgence Mansal

“…Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal.…”
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Existence of Solution via Integral Inequality of Volterra-Fredholm Neutral Functional Integrodifferential Equations with Infinite Delay by Kishor D. Kucche, Machindra B. Dhakne

“…To obtain a priori bounds of solutions required in Krasnoselski-Schaefer type fixed point theorem, we have used an integral inequality established by B. …”
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Existence Results for a Class of p-Laplacian Fractional Differential Equations with Integral Boundary Conditions by SunAe Pak, KumSong Jong, KyuNam O, HuiChol Choi

“…We obtain some existence and uniqueness results concerned with our problem by using Schaefer’s fixed-point theorem and Banach contraction mapping principle. …”
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Hilfer-Hadamard Nonlocal Integro-Multipoint Fractional Boundary Value Problems by Chanon Promsakon, Sotiris K. Ntouyas, Jessada Tariboon

“…The existence of a unique solution is obtained via Banach contraction mapping principle, while the existence results are established by applying Schaefer and Krasnoselskii fixed point theorems as well as Leray-Schauder nonlinear alternative. …”
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Existence and Ulam–Hyers stability results for Caputo–Hadamard fractional differential equations with non-instantaneous impulses by Mesfin Teshome Beyene, Mitiku Daba Firdi, Tamirat Temesgen Dufera

“…By employing Banach’s and Schaefer’s fixed-point theorems, we attain the required results. …”
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Boundary Value Problem for Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Impulses by Abdelkrim Salim, Mouffak Benchohra, Jamal Eddine Lazreg, Gaston N’Guérékata

“…The results are obtained using the Banach contraction principle and Krasnoselskii’s and Schaefer’s fixed-point theorems.…”
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Fractional-Calculus Analysis of the Dynamics of a Vector-Borne Infection with Preventive Measures by Rashid Jan, Salah Boulaaras, Asma Alharbi, Normy Norfiza Abdul Razak

“…In this paper, the proposed malaria model is analyzed both quantitatively and qualitatively. The fixed-point theorems of Banach and Schaefer are utilized to examine the uniqueness and existence of the solution dynamics. …”
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