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In this paper, we prove some existence and uniqueness results for some classes of deformable implicit fractional differential equations in b-Metric spaces with initial conditions. We base our arguments on some some fixed point theorems. Finally, we provide an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new inertial type algorithm with self -- adaptive step -- size technique for approximating a common element of the set of solutions of pseudomonotone variational inequality problem and the set of common fixed point of a finite family of generic generalized nonspreading mappings in uniformly smooth and 2 -- uniformly convex real Banach space. Furthermore, we prove a strong convergence theorem of our algorithm without prior knowledge of the Lipschitz constant of the operator under some mild assumptions. We also give numerical examples to illustrate the performance of our algorithm. Our result generalize and improve many existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of F--G--contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F--metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the existence of some solutions for a multi singular fractional differential system with some boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of nontrivial solutions for a fractional boundary value problem in Hölder spaces by a technical approach based on Leray-Schauder nonlinear alternative. Moreover, using the concept of orthogonal set on Banach fixed point theorem we obtain another existence result with weaker conditions. Also, recent results are extended and improved. In addition, we give some examples to illustrate the feasibility and effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, we use the concept of a generalized - Geraghty contraction type mapping to introduce the new notion of - Geraghty type F-contraction multivalued mapping and prove some new common fixed point results for such contraction in b-metric-like spaces. Also, we give some examples to illustrate our main results, we also discuss existence a solution for a system of non-linear integral equation. [ABSTRACT FROM AUTHOR]

In this paper we present some fixed point theorems for mappings satisfying contractive conditions on C*-algebra-valued b-metric spaces. Specifically we extend some fixed point results on metric spaces to C*-algebra valued case and prove the related fixed point theorems. Also several theorems in existence of n-periodic points are given. [ABSTRACT FROM AUTHOR]

We investigate the existence and uniqueness of the solution and also the rate of convergence of a numerical method for a fractional differential equation in both q-calculus and (p; q)-calculus versions. We use the Banach and Schauder fixed point theorems in this study. We provide two examples, one by definition of the q-derivative and the other by (p; q)-derivative. We compare the rate of convergence of the numerical method. We like to clear some facts on (p; q)-calculus. The data from our numerical calculations show well that q-calculus works better than (p; q)-calculus in each case. [ABSTRACT FROM AUTHOR]

In this work, we discuss the existence of solutions of infinite systems for a boundary value problem of Caputo fractional differential inclusions involving convex-compact multivalued maps. Our results are based on an appropriate fixed point theorem for condensing maps in the multivalued case. Eventually, we demonstrate an example to show the effectiveness and usefulness of the obtained result. [ABSTRACT FROM AUTHOR]