NONLOCAL INITIAL VALUE PROBLEMS FOR HILFER-TYPE FRACTIONAL HYBRID DIFFERENTIAL EQUATIONS WITH IMPULSE
D. VIVEK
Department of Mathematics, PSG College of Arts & Science, Coimbatore-641014, India.
K. KANAGARAJAN
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts & Science, Coimbatore-641020, India.
E. M. ELSAYED *
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this note, we verify the existence of solutions to nonlocal initial value problems for Hilfer-type fractional hybrid differential equations with impulsive condition. Then, we use prerequisites of Hilfer fractional calculus and the standard fixed point theorem due to Dhage for deriving the existence results in the weighted space of continuous functions. An example is presented to illustrate the theory results.
Keywords: Hilfer fractional derivative, Existence, Fixed point, Fractional hybrid differential equations.