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The subject of this work is the existence and Mittag-Leffler-Ulam (MLU) stability of solutions for fractional pantograph equations with three sequential fractional derivatives. Sufficient conditions for the existence and uniqueness of solutions are constructed by utilizing well-known classical fixed point theorems such as the Banach contraction principle, and Leray-Schauder nonlinear alternative. The generalized singular Gronwall's inequality is used to show the MLU stability results. An illustrated example is provided to support the main findings.

In the current manuscript, we consider a sequential q-fractional Lane-Emden system involving Riemann-Liouville and Caputo type fractional q-derivatives. We prove the uniqueness of solutions by means Banach fixed point theorems. Then, to demonstrate theexistence of at least one solution, we use Schaefer's fixed point theorem. Also we define and prove two types of Ulam-Hyers for the proposed system. Finally, an illustrative example is proposed. (2010) Mathematics Subject Classifications: 39A13, 39B72, 30C45.

This paper thinks about a nonlinear multi term q–differential conditions of arbitrary fractional orders. New existence and uniqueness comes about are built up utilizing Ba-nach contraction principle. Other existence results are gotten utilizing Schaefer and Krasnoselskii fixed point theorems. In organize to clarify our comes almost, some illustrative cases are in addition displayed. (2010) Mathematics Subject Classifications: 34A08, 34B16, 39A13.

In the current manuscript, we combine the q-fractional integral operator and q-fractional derivative to investigate a coupled hybrid fractional q-differential systems with sequential fractional q-derivatives. The existence and uniqueness of solutions for the proposed system are established by means of Leray-Schauder’s alternative and the Banach contraction principle. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability results are discussed. Finally, two illustrative examples are given to highlight the theoretical findings.

In this work, we establish some new (k, s) −fractional integral inequalities of continuous random variables by using the (k, s) −Riemann-Liouville fractional integral operator.

This paper studies the existence of solutions for Caputo fractional hybrid q-di¤erential equations. The existence obtained by using the Leray-Schauders alternative, while the uniqueness of solutions is established by means of Banachs contraction mapping principle. An illustrative examples are also included.

In this paper, we study existence, uniqueness and Ulam-Hyers stability of solutions for integro-differential equations involving two fractional orders. By using Banach's fixed point theorem, we obtain some sufficient conditions for the existence and uniqueness of solution for the mentioned problem. Furthermore, we derive the Ulam-Hyers stability and the generalized Ulam-Hyers stability of solution. At the end, an illustrative example is discussed.

In this paper, we establish new integral inequalities for continuous random variables. By introducing new concepts on fractional moments of continuous random variables, we generalize some interesting results of P. Kumar. Other fractional integral results are also presented. © 2018, Publishing House of the Romanian Academy. All rights reserved.

In this paper, we study existence and uniqueness of solutions for a coupled system of multi-point boundary value problems for fractional di¤erential equations. Applying principle contraction and Shaefer's fixed point theorem new existence results are obtained.

In this paper, we use the Hadamard fractional integral operator to establish some new weighted integral inequalities involving a family of n; (n ≥ 1) positive functions.

In this paper, the generalized Riemann-Liouville fractional integral operator is used to generate some new fractional integral inequalities. By using the generalized Riemann-Liouville fractional integral operator, we also generate new classes of fractional integral inequalities using a family of n, (n ≥ 1) positive functions.

In this paper, we have studied existence and uniqueness of solutions for a coupled system of multi-point boundary value problems for Hadamard fractional differential equations. By applying principle contraction and Shaefer's fixed point theorem new existence results have been obtained.

This paper studies a coupled system of two differential equations of arbitrary orders using Caputo approach with n derivatives, n є N *, n ≠ 1. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

In this paper, we discuss the existence, uniqueness and stability of solutions for a nonlocal boundary value problem of nonlinear fractional differential equations with two Caputo fractional derivatives. By applying the contraction mapping and O’Regan fixed point theorem, the existence results are obtained. We also derive the Ulam-Hyers stability of solutions. Finally, some examples are given to illustrate our results.

In this paper, we consider three point boundary value problem for fractional dierential equations of order 1 < < 2. We establish new conditions for the existence and uniqueness of solutions by using Banach xed point theorem. We also generate other existence results using Scheafer and Krasnoselskii xed point theorems.