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In this paper, we establish some new existence results for certain coupled systems of nonlinear Ψ-fractional differential equations with four-point fractional integral boundary conditions. The proofs are derived from Banach fixed point theorem. As an application, a nontrivial example is presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider integral boundary value problems of nonlinear fractional differential equations. Existence results of positive solutions for the problem are obtained based on the Guo-Krasnoselskii theorem and the Five functional fixed point theorem. Simple examples follow the main results in successive sections. [ABSTRACT FROM AUTHOR]

In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]

In this paper we give a classification of endomorphisms and additive mappings of a prime ring satisfying certain algebraic identities. Moreover, we provide an example proving that the primeness hypothesis imposed in our theorems is not superfluous. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of solutions for a tripled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the γ-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered. [ABSTRACT FROM AUTHOR]

In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time fractional diffusion equation with variable coefficients is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Inspired by the paper of Fazli and Nieto in [Open Math. 17 (2019) 499--512], we establish new existence and uniqueness result for a type of fractional Bagley--Torvik differential equation. Reported result not only generalizes previous results but also adopts different technique. We finish this study by concluding remarks which discuss the preference of our theorem compared to previous results. An example is constructed with specific parameters that requires weaker conditions for the existence of a unique solution. Meanwhile, we construct an iterative sequence that converges to the unique solution and can not be commented via the results of Fazli and Nieto. [ABSTRACT FROM AUTHOR]