ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF FRACTIONAL ORDER PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS

2017 ◽  
Vol 102 (1) ◽  
pp. 121-136
Author(s):  
Amina Kassim Hussain ◽  
Fadhel Subhi Fadhel ◽  
Nursalasawati Rusli ◽  
Zainor Ridzuan Yahya
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions

scholarly journals On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2106
Author(s):  
Seyfeddine Moualkia ◽  
Yong Xu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Variable Order ◽  
Uniqueness Of Solutions ◽  
Fractional Stochastic Differential Equations ◽  
Picard Iterations

Fractional stochastic differential equations are still in their infancy. Based on some existing results, the main difficulties here are how to deal with those equations if the fractional order is varying with time and how to confirm the existence of their solutions in this case. This paper is about the existence and uniqueness of solutions to the fractional stochastic differential equations with variable order. We prove the existence by using the Picard iterations and propose new sufficient conditions for the uniqueness.

On fractional order derivatives and Darboux problem for implicit differential equations

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Aleksandr Vityuk
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Fixed Point Theorems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Darboux Problem ◽  
Hyperbolic Differential Equations

AbstractIn this paper we prove some relations between the Riemann-Liouville and the Caputo fractional order derivatives, and we investigate the existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of functional hyperbolic differential equations by using some fixed point theorems.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

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