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EFFECT OF PERTURBATION IN THE SOLUTION OF FRACTIONAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
MOHAMMED. S. ABDO,SATISH. K. PANCHAL 한국산업응용수학회 2018 Journal of the Korean Society for Industrial and A Vol.22 No.1
In this paper, we study the initial value problem for neutral functional differential equations involving Caputo fractional derivative of order α ∈ (0, 1) with infinite delay. Some sufficient conditions for the uniqueness and continuous dependence of solutions are established by virtue of fractional calculus and Banach fixed point theorem. Some results obtained showed that the solution was closely related to the conditions of delays and minor changes in the problem. An example is provided to illustrate the main results.
EXISTENCE OF SOLUTION FOR IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS VIA TOPOLOGICAL DEGREE METHOD
TAGHAREED A. FAREE,SATISH K. PANCHAL 한국산업응용수학회 2021 Journal of the Korean Society for Industrial and A Vol.25 No.1
This paper is studied the existence of a solution for the impulsive Cauchy problem involving the Caputo fractional derivative in Banach space by using topological structures. We based on using topological degree method and fixed point theorem with some suitable conditions. Further, some topological properties for the set of solutions are considered. Finally, an example is presented to demonstrate our results.
WEIGHTED FRACTIONAL INEQUALITIES USING MARICHEV-SAIGO-MAEDA FRACTIONAL INTEGRAL OPERATOR
ASHA B. NALE,SATISH K. PANCHAL,VAIJANATH L. CHINCHANE 한국산업응용수학회 2021 Journal of the Korean Society for Industrial and A Vol.25 No.2
In this paper, we investigate several new weighted fractional integral inequalities by considering Marichev-Saigo-Maeda (MSM) fractional integral operator.
Nonlinear implicit fractional differential equation involving -Caputo fractional derivative
MOHAMMED S. ABDO,AHMED G. IBRAHIM,SATISH K. PANCHAL 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.3
In this paper, we consider a nonlinear implicit fractional dierential equation with nonlocal condition and involving the Caputo fractional derivative with respect to another function. We investigate the existence, uniqueness of solution on subinterval of the original interval. Hence we give an estimation for this solution. Further, we discuss the continuous dependence of solution involved in the problem. The results obtained by means of a variety of tools fractional calculus including Banach contraction mapping principle. Illustrative examples are also given.