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In this paper, we intend to investigate the solutions of the fractional differential inclusion system with successive derivatives with the Laplace operator and according to the derivative and integral boundary conditions. In this regard, we use the fixed point and end point theorems. Finally, we will show this device's effectiveness by providing some practical examples. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate, by applying the standard Caputo fractional q-derivative of order α, the existence of solutions for a class of the singular fractional q-integro-differential equation under some boundary conditions on a time scale. We consider the compact map and the Lebesgue dominated theorem for finding solutions of the problem. Our attention is concentrated on fractional multistep methods of both implicit and explicit type, for which sufficient existence conditions are investigated. Lastly, we present some examples involving graphs, tables and algorithms to illustrate the validity of our theoretical findings. [ABSTRACT FROM AUTHOR]

In the current work, we present some innovative solutions for the attractivity of fractional functional q-differential equations involving Caputo fractional q-derivative in a k-dimensional system, by using some fixed point principle and the standard Schauder's fixed point theorem. Likewise, we look into the global attractivity of fractional q-differential equations involving classical Riemann-Liouville fractional q-derivative in a k-dimensional system, by employing the famous fixed point theorem of Krasnoselskii. Also, we must note that, this paper is mainly on the analysis of the model, with numerics used only to verify the analysis for checking the attractivity and global attractivity of solutions in the system. Lastly, we give two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

Using the approximate endpoint property, we describe a technique for existing solutions of the fractional q-differential inclusion with boundary value conditions on multifunctions. For this, we use an approximate endpoint result on multifunctions. Also, we give an example to elaborate on our results and to present the obtained results by fractional calculus. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish some fixed point theorems for mappings with the contractive condition of integrable type on complete intuitionistic fuzzy metric spaces (X;M;N; *; ◊). We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of A-contraction mapping on metric space. In this paper by using the main idea of the work, we introduce the concept of A-fuzzy contractive mappings. Finally, we support our results by some examples. [ABSTRACT FROM AUTHOR]

In 2012, Samet, Vetro and Vetro introduced the notion of α-ψ-contractive mappings. They established some fixed point results for the mappings on complete metric spaces. In this paper by using main idea of the work, we introduce the concept of α-ψ-contractive mapping's on intuitionistic metric spaces and give some fixed point results about the mappings on complete intuitionistic metric spaces. Also, we give an application of our results about the existence of solution of a nonlinear fractional differential equation via a two-point boundary value condition. [ABSTRACT FROM AUTHOR]