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Full-Text Articles in Physical Sciences and Mathematics
A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson
A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson
Turkish Journal of Mathematics
In this article, we give sufficient conditions for the existence of solutions for a new coupled system of second-order implicit differential equations with Hadamard and Erdelyi-Kober fractional integral boundary conditions and nonlocal conditions at the boundaries in Banach space. The main result is based on a Mönch fixed point theorem combined with the measure of noncompactness of Kuratowski; an example is given to illustrate our approach.
Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal
Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal
Turkish Journal of Mathematics
The standard Caputo fractional derivative is generalized for the piecewise continuous functions. A more general boundary value problem for the impulsive Langevin fractional differential equation involving the Caputo fractional derivatives is studied. New existence results for solutions of concerned problems are established.
Nonexistence Of Global Solutions For A Fractional System Of Strongly Coupled Integro-Differential Equations, Ahmad Mugbil Ahmad, Nasser Eddine Tatar
Nonexistence Of Global Solutions For A Fractional System Of Strongly Coupled Integro-Differential Equations, Ahmad Mugbil Ahmad, Nasser Eddine Tatar
Turkish Journal of Mathematics
In this paper, we study the nonexistence of nontrivial global solutions for a system of two strongly coupled fractional differential equations. Each equation involves two fractional derivatives and a nonlinear source term. The fractional derivatives are of Caputo type of subfirst orders. The nonlinear sources are nonlocal in time. They have the form of a convolution of a polynomial of the state with a (possibly singular) kernel. The system under consideration is a generalization of many interesting special systems of equations whose solutions do not exist globally in time. We establish some criteria under which no nontrivial global solutions exist. …