Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

Abstract

A class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results.

Topological Structure of the Solution Sets for Impulsive Fractional Neutral Differential Inclusions with Delay and Generated by a Non-Compact Demi Group

“…For recent contributions on neutral differential inclusions of fractional order, Burqan et al [29] give a numerical approach in solving fractional neutral pantograph equations via the ARA integral transform. Ma et al [30] studied the controllability for a neutral differential inclusion with Hilfer derivative, and Etmad et al [31] investigated a neutral fractional differential inclusion of Katugampola-type involving both retarded and advanced arguments.…”

Qualitative Study on Solutions of a Hadamard Variable Order Boundary Problem via the Ulam–Hyers–Rassias Stability

“…Although this idea seems elementary and simple, it involves remarkable effects and outcomes which describe many physical and natural phenomena accurately. For this reason, research into both of the theoretical and practical aspects of boundary value problems has attracted the focus of many mathematicians in international academic institutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. A main difference and novelty in this investigation is the application of the concept of variable order operators.…”

A q-Gradient Descent Algorithm with Quasi-Fejér Convergence for Unconstrained Optimization Problems

“…Besides appearing as a connection between mathematics and physics, q-calculus has many applications in different mathematical areas such as operator theory [12], combinatorics [13], orthogonal polynomials [14], basic hyper-geometric functions [15], and other sciences like quantum theory [16,17], mechanics [18], and fractional calculus [19][20][21][22][23][24][25]. For more recent studies about fractional calculus analysis and applications, refer to [26][27][28][29][30][31].…”